Optical core networks using OFDM signals

Optical core networks using OFDM signals

Filipe Manuel Wiener Ferro de Carvalho

Dissertação para obtenção do Grau de Mestre em

Engenharia Electrotécnica e de Computadores

Júri

Presidente: Prof. José Manuel Bioucas DiasOrientador: Prof. Adolfo da Visitação Tregeira CartaxoCo-orientador: Dr. Daniel Diogo da Trindade FonsecaVogal: Prof. António Luís Jesus Teixeira

Novembro 2009

Acknowledgments

First of all, I would like to thank my supervisor, Professor Adolfo Cartaxo, for his great availability to

supervise my work and answer my questions, as well as providing me with material and literature to

develop and write this work.

I would like to thank my co-supervisor, Dr. Daniel Fonseca at Nokia Siemens Networks, for providing

me the technical information on the WSS, for his availability to answer my questions and to review this

work.

I would like to thank my family for their support, which was fundamental for the realization of this work.

I would like to thank also Instituto de Telecomunicações (IT) for providing me access to their installations

and for the monthly scholarship.

I thank also the PhD students at the Group of Research on Optical Fibre Telecommunications Systems

(GROFTS) of IT-Lisboa, Nelson da Costa and Tiago Alves, for their availability to answer my questions

and helping me with the simulation equipment.

i

Abstract

The main objective of this dissertation is to study the limitations, associated with bandwidth narrowing,

of employing reconfigurable optical add-drop multiplexers (ROADM) on core networks using orthogonal

frequency division multiplexing (OFDM) signals at 100 Gbps.

A study of the core networks and their characteristics, as well as of the OFDM signals that best adapt to

these networks (coherent optical OFDM – CO-OFDM), is performed. Two transmission systems using

CO-OFDM are designed, one transmitting one full data rate CO-OFDM signal and the other transmitting

two half data rate CO-OFDM signals, each one in a different polarization direction using polarization

division multiplexing (PDM).

The ROADM used in this work is studied and two models are developed. The simple model takes only

into account the filtering effect due to the wavelength selective switch (WSS) and the dispersive model

takes also in consideration the dispersion added by the real device.

Finally, the performance of the two transmission systems, using the models developed for the ROADM,

are analysed by means of numeric simulation using MATLAB.

The ability of CO-OFDM systems to compensate for the dispersion added by the maximum length of

optical fibre to which the system was designed is shown for both systems. It is also shown that the

bandwidth narrowing due to a chain of those ROADMs has a reduced impact on the performance of the

CO-OFDM signals transmitted. The performance limiting factor are the losses each of those ROADMs

introduces on the optical link.

Keywords: optical fibre, core-networks, 100 Gbps, orthogonal frequency division multiplexing, coherent

optical OFDM, reconfigurable optical add-drop multiplexers

ii

Resumo

O principal objectivo desta dissertação é estudar as limitações associadas ao estreitamento de banda dev-

idas aos multiplexadores ópticos de inserção-extracção reconfiguráveis (ROADMs) em redes de núcleo,

usando sinais de multiplexagem ortogonal por divisão na frequência (OFDM) a 100 Gbps.

Estudam-se as redes de núcleo e suas características, bem como o tipo de sinais OFDM que melhor se

adequa àquelas redes (OFDM óptico coerente – CO-OFDM). São projectados dois sistemas de trans-

missão usando CO-OFDM: um transmite o débito total num único sinal CO-OFDM, enquanto o outro

transmite dois sinais CO-OFDM a metade do débito total, cada um numa direcção de polarização, usando

multiplexagem por divisão na polarização (PDM).

A partir de um estudo dos ROADMs usados neste trabalho, são desenvolvidos dois modelos para os

ROADMs. O modelo simples leva em conta o efeito de filtragem introduzido pelos comutadores por

selecção de comprimento de onda (WSS), enquanto o modelo dispersivo considera também a dispersão

introduzida por estes dispositivos.

Por último, é analisado o desempenho dos dois sistemas de transmissão, usando os modelos do ROADM

desenvolvidos para o efeito, recorrendo a simulação numérica em MATLAB.

É demonstrada a capacidade dos dois sistemas CO-OFDM em compensar os efeitos da dispersão para o

máximo comprimento de fibra para que foram dimensionados. Demonstra-se, também, que a largura de

banda da cadeia dos ROADMs considerados tem pouco impacto no desempenho dos dois sistemas deste

trabalho usando sinais CO-OFDM, enquanto o factor limitador do desempenho são as perdas que cada

ROADM introduz na ligação.

Palavras-chave: fibra óptica, redes de núcleo, 100 Gbps, multiplexagem ortogonal por divisão na fre-

quência, OFDM óptico coerente, multiplexadores ópticos de inserção-extracção reconfiguráveis

iii

Contents

Acknowledgments i

Abstract ii

Resumo iii

Contents iv

List of figures viii

List of tables xi

List of acronyms xii

List of symbols xv

1. Introduction 1

1.1. Scope of the work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1. Capacity demands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.2. Transport solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3. System specific details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3.1. Telecommunication network and optical systems . . . . . . . . . . . . . . . . . 4

1.3.2. Optical core networks characteristics and challenges . . . . . . . . . . . . . . . 7

1.4. Optical signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.4.1. Optical signals at 100 Gbps . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.4.2. Optical OFDM signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.4.3. Trade-offs and limitations in optical OFDM . . . . . . . . . . . . . . . . . . . . 9

1.5. Objectives and dissertation organization . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.6. Main contributions of this work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

iv

2. System description 13

2.1. OFDM signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1.1. Basics of OFDM signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1.2. General concepts for OFDM transmission . . . . . . . . . . . . . . . . . . . . . 14

2.2. CO-OFDM transmission system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2.1. OFDM signal coder and decoder . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2.2. Coherent optical transmitter and receiver . . . . . . . . . . . . . . . . . . . . . 20

2.2.3. CO-OFDM transmitter and receiver . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2.4. Technical assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2.5. Technical parameters of the CO-OFDM system . . . . . . . . . . . . . . . . . . 23

2.3. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3. Description of in-line components 27

3.1. Optical fibre . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2. Optical amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3. ROADM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3.1. Wavelength selective switch . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3.2. WSS - simplified model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.3.3. WSS - model with dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.4. Effects of a chain of ROADMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4. Results and discussion 37

4.1. System performance for a given OSNR (using a noise loader) . . . . . . . . . . . . . . . 37

4.1.1. System without ROADMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.1.2. System with ROADMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.2. System performance in a real optical link . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.3. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5. Conclusions and future work 45

5.1. Final conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.2. Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6. Bibliography 47

A. Details of the OFDM coder and decoder 53

A.1. Constellation mappers and symbol detectors . . . . . . . . . . . . . . . . . . . . . . . . 53

v

A.2. DAC and ADC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

A.2.1. Digital to analog conversion fundamentals . . . . . . . . . . . . . . . . . . . . . 54

A.3. SH, LPF and ADC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

A.4. Pre-emphasis and equalizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

A.4.1. Pre-emphasis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

A.4.2. Equalizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

A.5. CP and training symbol modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

A.6. IFFT+P/S and S/P+FFT modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

A.7. OFDM symbol synchronisation at the decoder . . . . . . . . . . . . . . . . . . . . . . . 63

B. Elements of the coherent optical transmitter and receiver 67

B.1. Optical and electrical components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

B.1.1. Directional coupler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

B.1.2. Optical modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

B.1.3. Optical source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

B.1.4. Optical filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

B.1.5. Photodetector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

B.2. Transmitted signal equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

B.3. Received signal equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

B.4. Confirmation of analytical results by simulation . . . . . . . . . . . . . . . . . . . . . . 74

B.5. Optical synchronisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

C. Typical OFDM parameters used in CO-OFDM systems and system design 77

D. Noise, OSNR and BER 81

D.1. Noise generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

D.2. OSNR in the simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

D.2.1. OSNR and SNR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

D.2.2. OSNR measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

D.2.3. OSNR imposition technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

D.3. BER estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

E. Validation of CO-OFDM signal simulator 89

E.1. Back-to-back configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

E.2. Fibre chromatic dispersion compensation . . . . . . . . . . . . . . . . . . . . . . . . . 90

E.3. Replication of experiment 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

vi

E.4. Replication of experiment 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

E.5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

F. Cyclic prefix, postfix and their performance 93

vii

List of Figures

1.1. Architecture of a telecommunication network hierarchy and how the core, metropolitan,

regional, access and domestic networks interconnect. . . . . . . . . . . . . . . . . . . . 5

2.1. OFDM signal in time domain and in frequency domain . . . . . . . . . . . . . . . . . . 14

2.2. Scheme of the OFDM stream used in this work. . . . . . . . . . . . . . . . . . . . . . . 15

2.3. Examples of OFDM systems using: cyclic prefix, cyclic postfix and cyclic extension. . . 16

2.4. Scheme of the OFDM coder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.5. Scheme of the OFDM decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.6. Scheme of the coherent optical transmitter (CO-TX). . . . . . . . . . . . . . . . . . . . 20

2.7. Scheme of the coherent optical receiver (CO-RX). . . . . . . . . . . . . . . . . . . . . . 21

2.8. Scheme of transmission system no. 1 and no. 2. . . . . . . . . . . . . . . . . . . . . . . 22

3.1. ROADM simplified scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.2. Ideal WSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3. Transfer function retrieved experimentally from the WSS . . . . . . . . . . . . . . . . . 32

3.4. Transfer function of the modeled WSS . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.5. Transfer function of a chain of ROADMs for one WDM channel. . . . . . . . . . . . . . 35

3.6. Noise power evolution along the line. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.1. Performance comparison of systems no. 1 and no. 2, without ROADMs. . . . . . . . . . 37

4.2. Performance comparison of system no. 1 with and without ROADMs. . . . . . . . . . . 39

4.3. Performance comparison of system no. 2 with and without ROADMs. . . . . . . . . . . 39

4.4. Evolution of the OSNR per OFDM stream, along the optical link. . . . . . . . . . . . . 41

4.5. Performance comparison of system no. 1 versus system no. 2. . . . . . . . . . . . . . . 42

A.1. Scheme of the implemented constellation mapper and used constellation. . . . . . . . . . 53

A.2. Scheme of the symbol detector implemented, used constellation and received data symbol. 54

A.3. Example of the digital to analog conversion implemented in the simulator. . . . . . . . . 55

A.4. Power spectral density of the signal at the output of the SH, for an input of AWGN. . . . 55

viii

A.5. OFDM signals in frequency, using 60 % of its sub-carriers and using 90 % of its sub-

carriers, respectively . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

A.6. Gain of a 6th order Bessel LPF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

A.7. Scheme of the implemented ADC method. . . . . . . . . . . . . . . . . . . . . . . . . . 57

A.8. Pre-emphasis and equalization techniques. . . . . . . . . . . . . . . . . . . . . . . . . . 58

A.9. Pre-emphasis and equalization techniques where noise is added together with the distortion. 59

A.10.OFDM signal generated by a SH, after a LPF using pre-emphasis, after a LPF without

using pre-emphasis and directly out of the SH. . . . . . . . . . . . . . . . . . . . . . . . 59

A.11.Scheme of the implemented CP-module. . . . . . . . . . . . . . . . . . . . . . . . . . . 61

A.12.Scheme of the implemented IFFT+P/S module. . . . . . . . . . . . . . . . . . . . . . . 62

A.13.Scheme of the implemented S/P+FFT module. . . . . . . . . . . . . . . . . . . . . . . . 62

A.14.Timing metric obtained for a stream of OFDM frames and one of its peaks is shown in a

greater scale. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

A.15.Scheme of the symbol synchroniser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

A.16.Special charactheristic of training symbols for the Schmidl and Cox algorithm . . . . . . 65

A.17.Scheme of TSQ and TS generation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

B.1. Scheme of the directional coupler. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

B.2. Scheme of a MZM modulator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

B.3. Optical filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

B.4. Optical filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

B.5. Confirmation of equations B.32 and B.33 by simulation. . . . . . . . . . . . . . . . . . 75

B.6. Phase determination algorithm at coherent optical receiver. . . . . . . . . . . . . . . . . 76

C.1. Bandwidth of OFDM stream signal carrying a bit rate of 112 Gbps and 56 Gbps. . . . . 78

C.2. Duration of guard interval for system no. 1 and no. 2 . . . . . . . . . . . . . . . . . . . 79

D.1. Generation of AWGN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

D.2. Generation of noise at an EDFA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

D.3. SNR on both systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

D.4. OFDM stream signal spectrums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

D.5. Example of PSD of the received signal at the input of the receiver in the simulation. . . . 85

D.6. Example of measurement of Ps and Pn−re f in the simulator . . . . . . . . . . . . . . . . 86

D.7. Example of OSNR imposition in the simulator . . . . . . . . . . . . . . . . . . . . . . . 87

D.8. Direct error count scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

ix

E.1. Received constellation using system no. 2 in a back-to-back configuration. . . . . . . . . 89

E.2. System no. 2 received constellation for several lengths of SSMF. . . . . . . . . . . . . . 90

F.1. Response of different lengths of SSMF to a Dirac impulse. The propagation time was

not considered. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

F.2. Transmission with CP and CPF (CE) and only with CP over a dispersive channel. . . . . 95

F.3. Performance comparison between three versions of system no. 2, (using empty guard

intervals, CP and CE). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

x

List of Tables

1.1. Comparison of the characteristics of the several layers of a telecommunication network

[Par08], [Sal99], [Lee06] and [Chan08]. . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1. Parameters of the two system variants, no. 1 and no.2. . . . . . . . . . . . . . . . . . . . 24

3.1. Bandwidth narrowing in a cascade of ROADMs . . . . . . . . . . . . . . . . . . . . . . 34

C.1. Typical values used in CO-OFDM systems. . . . . . . . . . . . . . . . . . . . . . . . . 77

C.2. Target parameters of the two variants of the OFDM transport system analysed in this work. 78

C.3. Parameters of both systems 1 and 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

C.4. Bandwidths of the filters used in the system for both variants system no. 1 and no. 2. . . 80

E.1. Parameters gathered from [Shi07] and the parameters used in the simulator. . . . . . . . 91

E.2. Parameters gathered from [Jan09] and the parameters used in the simulator. . . . . . . . 91

xi

List of acronyms

100 GbE . . . . . . . . 100 Gigabit Ethernet

AC . . . . . . . . . . . . . Alternating Current

ADC . . . . . . . . . . . Analog-to-Digital-Converter

ASE . . . . . . . . . . . . Amplified Spontaneous Emission

ATM . . . . . . . . . . . Asynchronous Transfer Mode

AWG . . . . . . . . . . . Arbitrary Waveform Generator

AWGN . . . . . . . . . Additive White Gaussian Noise

BER . . . . . . . . . . . . Bit Error Rate

CE . . . . . . . . . . . . . Cyclic Extension

CO-OFDM . . . . . . Coherent Optical Orthogonal Frequency Division Multiplexing

CP . . . . . . . . . . . . . . Cyclic Prefix

CPF . . . . . . . . . . . . Cyclic PostFix

DAC . . . . . . . . . . . . Digital-to-Analog Converter/Conversion

DB . . . . . . . . . . . . . Duo-Binary

DDO-OFDM . . . . Direct Detection Optical Orthogonal Frequency Division Multiplexing

DEC . . . . . . . . . . . . Direct Error Counting

DFT . . . . . . . . . . . . Discrete Fourier Transform

DQPSK . . . . . . . . . Differential Quadrature Phase Shift Keying

DS . . . . . . . . . . . . . Data Symbol

DSP . . . . . . . . . . . . Digital Signal Processor

DWDM . . . . . . . . . Dense Wavelength Division Multiplexing

EDFA . . . . . . . . . . . Erbium Doped Fibre Amplifier

FEC . . . . . . . . . . . . Forward Error Correction

FFT . . . . . . . . . . . . Fast Fourier Transform

xii

FSS . . . . . . . . . . . . . Fine Symbol Synchroniser

FT . . . . . . . . . . . . . . Fourier Transform

FTTH . . . . . . . . . . . Fibre To The Home

GVD . . . . . . . . . . . Group Velocity Dispersion

ICI . . . . . . . . . . . . . Inter-Carrier Interference

IDFT . . . . . . . . . . . Inverse Discrete Fourier Transform

IP . . . . . . . . . . . . . . Internet Protocol

ISI . . . . . . . . . . . . . . Inter-Symbol Interference

LC . . . . . . . . . . . . . Liquid Crystal

LPF . . . . . . . . . . . . Low-Pass Filter

M-QAM . . . . . . . . M-ary Quadrature Amplitude Modulation

MCM . . . . . . . . . . . Multi-Carrier Modulation

MEM . . . . . . . . . . . Micro-Electro-Mechanical

MZM . . . . . . . . . . . Mach-Zehnder Modulator

NRZ . . . . . . . . . . . . Non-Return to Zero

NZDSF . . . . . . . . . Non-Zero Dispersion Shifted Fibre

OA . . . . . . . . . . . . . Optical Amplifier

OADM . . . . . . . . . Optical Add-Drop Multiplexer

OF . . . . . . . . . . . . . Optical Filter

OFDM . . . . . . . . . . Orthogonal Frequency Division Multiplexing

OOK . . . . . . . . . . . On-Off Keying

OSA . . . . . . . . . . . . Optical Spectrum Analyser

OSNR . . . . . . . . . . Optical Signal-to-Noise Ratio

OXC . . . . . . . . . . . . Optical Cross-Connect

P/S . . . . . . . . . . . . . Parallel-to-Serial

PAPR . . . . . . . . . . . Peak-to-Average Power Ratio

PD . . . . . . . . . . . . . Polarization Demultiplexer

PDL . . . . . . . . . . . . Polarization Dependent Loss

PDM . . . . . . . . . . . Polarization Division Multiplexing

PM . . . . . . . . . . . . . Polarization Multiplexer

PM-DQPSK . . . . . Polarization Multiplexing Differential Quadrature Phase Shift Keying

xiii

PMD . . . . . . . . . . . Polarization-Mode Dispersion

PON . . . . . . . . . . . . Passive Optical Network

PS . . . . . . . . . . . . . . Pilot Sub-carriers

QPSK . . . . . . . . . . Quadrature Phase-Shift Keying

ROADM . . . . . . . . Reconfigurable Optical Add-Drop Multiplexer

RZ . . . . . . . . . . . . . Return to Zero

S/P . . . . . . . . . . . . . Serial-to-Parallel

SC . . . . . . . . . . . . . . Schmidl and Cox

SDH . . . . . . . . . . . . Synchronous Digital Hierarchy

SH . . . . . . . . . . . . . Sample and Hold

SNR . . . . . . . . . . . . Signal-to-Noise-Ratio

SSMF . . . . . . . . . . Standard Single Mode Fibre

TS . . . . . . . . . . . . . . Training Symbols

TSQ . . . . . . . . . . . . Training SeQuence

ULH . . . . . . . . . . . . Ultra Long Haul

VSB . . . . . . . . . . . . Vestigial Side Band

WDM . . . . . . . . . . Wavelength Division Multiplexing

WRSS . . . . . . . . . . Wide Range Symbol Synchroniser

WSS . . . . . . . . . . . . Wavelength-Selective Switch

xiv

List of symbols

Bo f dm bandwidth of the OFDM signal

Bre f reference bandwidth for noise, typically 0.1 nm, or 12.5 GHz at 1550 nm

Bsim simulation bandwidth

c′(k, i) data symbol of the kth sub-carrier on the ith OFDM symbol at the output of the pre-emphasis

module

c(k, i) transmitted data symbol at the kth sub-carrier on the ith OFDM symbol at the output of the

constellation mappers

ct(k) training symbol at the kth sub-carrier of the training sequence saved at the OFDM decoder mem-

ory

cTs ratio between guard interval duration (Gi) and OFDM symbol duration (Ts)

d index of the dth sample of the digitalized received OFDM signal r[d]

Db Bit-rate per OFDM stream

dbg sample index of the received signal in which the TS of a given OFDM frame begins

Dλ fibre dispersion parameter

e f ors(t) electrical field of the optical signal at the output of the optical filter at the receiver

eI(t) electrical field of optical signal at the transmitter carrying the I channel

Eld1 absolute value of the electrical field of the signal generated by optical source LD1

eLD1(t) electrical field of optical signal generated at the coherent optical transmitter by source LD1

Eld2 absolute value of the electrical field of the signal generated by optical source LD2

eLD2(t) electrical field of optical signal generated at the coherent optical receiver by source LD2

eLD(t) electrical field of the 90o phase-shifted version of optical signal eLD2

Eldr absolute value of the electrical field of the optical signal at the input of the coherent optical

receiver

xv

eLI(t) electrical field of the optical carrier used by the MZM of the I channel before modulation

eLQ(t) electrical field of the optical carrier used by the MZM of the Q channel before modulation

emos(t) electrical field of the complete modulated optical signal at the output of the transmitter, carrying

the I and Q channels

eors(t) electrical field of the optical signal at the input of the coherent optical receiver

epin1(t) electrical field of the optical signal at the input of PIN 1 in the coherent optical receiver




eQ(t) electrical field of optical signal at the transmitter carrying the Q channel

er1(t) electrical field of the 0o phase-shifted version of optical signal e f ors(t)

er2(t) electrical field of the 90o phase-shifted version of optical signal e f ors(t)

fk frequency of the sub-carrier number k of the OFDM symbol

Fn amplifier noise figure in linear units

fs bandwidth of an OFDM system using 100% of the sub-carriers

ged f a gain of the EDFA in linear units

Gi guard interval between consecutive OFDM symbols

GI transimpedance gain used at the coherent optical receiver for the current ipinI in order to retrieve

the I channel

GQ transimpedance gain used at the coherent optical receiver for the current ipinQ in order to retrieve

the Q channel

h Planck constant = 6.62606896(33) ⋅10−34J ⋅ s

HE(k, i) value of the equalization function at the kth sub-carrier for the ith OFDM symbol used at the

OFDM decoder

Hg−0 gain of the WSS at the centre frequency of the channel in linear units

H(k, i) transmission channel frequency response for the kth OFDM sub-carrier during the ith OFDM

symbol

i index number of the OFDM symbol in the OFDM stream

xvi

Ich(t) electrical signal generated by the OFDM coder carrying the I channel

ipin(t) photocurrent produced by a PIN photo-diode

ipin1(t) photocurrent at the output of PIN 1




ipinI(t) current carrying signal Ich

ipinQ(t) current carrying signal Qch

k index number of the OFDM sub-carrier

Lkm total length of the optical link in km

LL last sub-carrier with data before the oversampling guard band at the negative side of the fre-

quency spectrum

LR last sub-carrier with data before the oversampling guard band at the positive side of the frequency

spectrum

Lsec length of each fibre span in km

Nb number of bits transmitted on each sub-carrier on one OFDM symbol

NCP length of the cyclic prefix in samples

NCPF length of the cyclic postfix in samples

ng order of the super-Gaussian function

Nn−x spectral density of noise at each OFDM stream signal in system no. x

Nsc total number of sub-carriers of the OFDM system

Nsp number of data symbols contained in one OFDM frame

nsp spontaneous emission factor (or population-inversion factor) of the EDFA

Nt length of the complete OFDM symbol (with CP/CPF/CE) in samples

Nu number of non-nulled sub-carriers used for data transmission

Nx(t) electrical field of the ASE noise on polarization direction ex

Ny(t) electrical field of the ASE noise on polarization direction ey

Pn−ed f a power of the noise added by each EDFA in W per polarization direction

xvii

Pn−re f optical noise power in the reference bandwidth

ppin(t) optical power of a signal illuminating a PIN photo-diode

Ps optical power of the signal of interest

q(t) OFDM signal with cyclic extension

Qch(t) electrical signal generated by the OFDM coder carrying the Q channel

r[d] digitalized received OFDM signal

S dispersion slope of the optical fibre

s(t) OFDM signal

Se spectral efficiency of the OFDM signal

sh f expansion factor of number of samples used between the digital and

analog world

sl speed of light in vacuum = 2.99792458 ⋅108 m/s

su ratio between used sub-carriers and FFT size in the OFDM system

td delay spread of the transmission channel

Ts duration of OFDM symbol

vπ voltage that must be present between the electrodes of the MZM in order to achieve a phase

difference of π between the two arms of the MZM

vdc MZM bias voltage

vr f (t) AC coupled electrical modulating signal applied to the MZM

y(k, i) received data symbols extracted directly from the FFT at the decoder before equalization

αdB fibre loss in dB/km

β (ω) propagation constant as a function of the frequency

∆ f frequency spacing between consecutive sub-carriers of the OFDM signal

∆ω frequency difference in radians, between the optical frequency, ν , and the central optical fre-

quency, ν0, at which the signal bandwidth is centered

xviii

∆φ(t) phase difference between the received optical signal and the optical signal generated at the re-

ceiver

λ0 central optical wavelength of the OFDM band

ν optical frequency in Hz

ν0 central optical frequency of the OFDM band

νc half of the 3-dB bandwidth of the super-Gaussian filter

φ1 initial phase of the signal generated by optical source LD1

φ2 initial phase of the signal generated by optical source LD2

φE phase of the optical signal at the input of the coherent optical receiver

ω1 angular frequency of the signal generated by optical source LD1

ω2 angular frequency of the signal generated by optical source LD2

xix

1. Introduction

In this chapter, the evolution of lightwave systems, as well as the characteristics and actual challenges of

optical networks (with special attention to optical core networks and 100 Gbps channels) are presented.

The scope of the work is presented in section 1.1. Section 1.2 presents the motivation, explains the

need for 100 Gbps channels and presents transport solutions for such channels. Section 1.3 presents the

characteristics of optical networks and section 1.4 the adequate optical signals to operate in the core part

of those networks. In sections 1.5 and 1.6 the objectives and the contributions of this work are presented,

respectively.

1.1. Scope of the work

In the mid-60’s, the ever growing voice traffic on the network and the known limitations of copper cables

to support the needed bandwidth triggered the search for a new transmission solution [Kec00]. The mi-

crowave radio links were already overloaded and some researchers pursued higher frequencies in search

for more bandwidth. In 1970, the first optical fibres with losses below 20 dB/km were invented and,

due to its advantages face to the cooper cables ( such as lower attenuation, broader bandwidth, lower

cross talk and reduced diameter and weight), these fibres began later that year to replace coaxial cables

in the trunk systems of telecommunication networks [O’M08]. The deployment of new optical systems

proceeded, as Internet started at the end of the 80’s to generate data traffic (causing a further increase in

traffic growth rate). During these years, millions of kilometres of optical fibre were deployed world wide

[Ped02]. As a result, fibre optical cables became the dominant transmission medium in the telecommuni-

cation network. The access network (see figure 1.1 where the position of the access network in the whole

telecommunication network is shown) is an exception, where traditional twisted pair cooper cables are

still in use. The cooper cables will be replaced by optical fibres in the expected future deployment of

broadband optical access, also known as fibre to the home (FTTH) [Des06].

The optical transmission systems had a huge technological development since their invention. From

1985 to 2002, three significant components where added to optical links/networks and those are: the

erbium doped fibre amplifier (EDFA), the reconfigurable optical add/drop multiplexer (ROADM) and

1

the optical cross connect (OXC) [Par08]. The EDFA allows to completely compensate for the optical

attenuation introduced by the optical fibre and other optical components. This enables longer distances

between regenerators, which reduces the cost per kilometre [Des06]. With a ROADM, it is possible to

extract and/or add some optical channels at a node, while bypassing the remaining channels in the opti-

cal domain and thereby spare unnecessary optical-to-electrical conversions. The configuration of which

channels to extract and/or to add can be remotely changed what brings operational advantages [Feu08].

An OXC switches optical channels from its input ports to the output ports. The advantages of the OXC

relative to the equivalent electronic equipment are reduced size and power [O’M08]. Another technolog-

ical breakthrough was the increase of capacity per fibre by the use of wavelength division multiplexing

(WDM). This multiplexing scheme is widely used on nowadays networks [Par08]. The economic de-

ployment of WDM was only possible due to the introduction of optical amplification [O’M08]. The

deployment of EDFA and WDM strongly contributed respectively to the increase of optical transmission

reach (which nowadays exceeds the normal distance between nodes on the network) and to the increase

of the amount of traffic carried by a fibre (which is much larger than the traffic terminating at any single

node) [Feu08]. For these two reasons, it is desirable for nodes to have switching/add/drop capabilities at

optical level. This led to the development of optical add/drop multiplexers (OADM) first, and then later

to the development of ROADMs. OXCs can switch a WDM channel of any input port to any output port.

OXCs are implemented by ROADMs that are based on a multiport wavelength-selective switch (WSS).

The scope of this work is to study the impact of optical networks that use chains of network elements

(such as ROADM and EDFA) in the performance of the optical signals transmitted.

1.2. Motivation

1.2.1. Capacity demands

Although the Internet is the one of the most recent traffic sources in the network (its deployment did

not happen more than 30 years ago [Cof02]), the traffic it generates has a higher growth ratio than any

other client segment (such as voice or data transaction). The result is that since the year 2000, the internet

protocol (IP) data is the dominating data type flowing in the global-network [Des06]. As a result, the total

traffic has been growing approximately at the rate of the IP traffic, which has consequences on the rate

of deployment of transmission capacity. Even if the projected growth rates of the IP traffic vary between

authors [Des06],[Cvi08], the increase of demand of capacity is certain. How can then the increase of

transport capacity be achieved? Deploy more fibres might be the first solution that comes to mind. It

increases the system capacity and redundancy, but at high costs, because building a complete new path

2

for a fibre to be deployed is complicated and expensive. On most cases, these fibres use (when possible)

the already existing infrastructures (such as subway tunnels, highways, rail tracks and water pipes) to

be installed and the right of passage is then bought to these infrastructure owners. Increase the number

of WDM channels might be the second solution. It brings great cost-savings and increases the capacity

of each fibre enormously (up to hundreds of WDM channels [ITUG694]). But in WDM, the spectral

efficiency is reduced due to the guard band between the channels and the smaller the guard band, the

greater will the cross-talk between channels be. The last option is to increase the data rate per channel.

It increases the capacity of the system with better spectral efficiency than the use of WDM channels. But

equipment to work at high data rates can be difficult to implement [Lam08] and the broadening of the

bandwidth (as a result of a higher data rate) increases the effects of: (1) fibre group velocity dispersion

(GVD), (2) polarization-mode dispersion (PMD) and (3) fibre nonlinearities on the data channel. These

effects limit the length and data rate of an optical fibre link [Zys02], and pose a problem in longer or

higher data rate links. The first solution mentioned (deploying more fibres), due to financial reasons

and deployment time is a last resort solution. The second solution (increasing the number of WDM

channels) solves the capacity problem on a short term. But on the long run, it will lead to an excessive

high number of parallel channels, resulting in a excessive high number of paths to monitor and restore

in case of hardware failure and also on a high number of electrical-optical components (such as lasers,

modulators and receivers) [Ess02]. This will result in higher costs and demands for another solution.

The third solution (increasing the data rate per channel), despite the technological challenges, does not

pose the disadvantages of the first two solutions and is therefore, in long term, the best solution.

1.2.2. Transport solutions

In order to transport huge amounts of IP data, Ethernet is considered to be one cost-effective mean

[Nak08] and several Ethernet generations have been deployed [Cvi08], from 10 Megabit Ethernet up to

10 Gigabit Ethernet (the bit rate of a new Ethernet generation is traditionally 10 times that of the previous

generation [Lam08]). Although synchronous digital hierarchy (SDH) was designed for voice traffic, it

can also transport data traffic. Traditionally, the bit rate of a new SDH generation is 4 times that of the

previous generation. This might bring some doubts about what should the bit rate of the next transport

technology be. Should it be 160 Gbps (following the SDH upgrade rule) or should it be 100 Gbps

(following the Ethernet rule)? Due to the ever growing dominant position of data traffic it makes sense

to use the system that best suits this data transmission, what points to Ethernet and thus to 100 Gbps per

channel [Har09]. Besides, limitations of the electronics make the implementation of 100 Gbps easier

to achieve than of the 160 bps [Lam08]. For these reasons, there is currently for approval a proposal

for a new Ethernet standard for IP networks, the 100 Gigabit Ethernet (100 GbE), which is expected to

3

become the next Ethernet standard [Cvi08]. As a result, there has been currently a lot of investigation on

transport solutions for 100 GbE [Win05], [Win08-Oct], [Jan09]. It is worth mentioning that a transport

solution for 100 GbE, due to expected forward error correction (FEC) and Ethernet protocol overheads

of about 7% and 4% respectively, needs to have a data rate of about 111 Gbps [Jan09].

1.3. System specific details

1.3.1. Telecommunication network and optical systems

A scheme of the telecommunication network is presented in figure 1.1. As it is there shown, the telecom-

munication network is hierarchically divided in three sub-networks: access, metropolitan/regional and

core (also known as backbone). The access network makes the interface between the end-user and the

telecommunication network. The central offices terminating the access network aggregate the traffic ad-

dressed to other central offices and pass it to the metropolitan or to the regional network, depending if

the area is a (sub)urban or rural one, respectively. The metropolitan network aggregates high tributary

traffic from the central offices, passes the traffic addressed to other metropolitan/regional areas to the

core network and delivers the remaining traffic to the respective destination central office [Cai07]. The

core network interconnects all the metropolitan/regional networks of a country and the international core

network interconnects countries and continents between themselves. As referred previously, the optical

fibres use extends to all network layers. Thus the characteristics of each optical network layer are now

presented. The optical access network is characterised by [Par08], [Sal99] :

∙ being passive (passive optical network-PON),

∙ high granularity (each stream of data is often individual, little aggregation),

∙ high fluctuation in traffic flow (due to the high granularity),

∙ operating with a wide variety of protocols such as IP, asynchronous transfer mode (ATM) and

Ethernet,

∙ covering small distances,

∙ having a wide variety of topologies implemented.

Metropolitan optical networks are characterised by [Par08], [Sal99] :

∙ having active elements (using optical amplification and optical add/drop granularity),

4

Figure 1.1.: Architecture of a telecommunication network hierarchy and how the core, metropolitan, re-gional, access and domestic networks interconnect.

5

∙ medium granularity (most streams of data result from aggregation of several users),

∙ medium fluctuation in traffic flow (due to aggregation), operating with a narrower variety of pro-

tocols,

∙ covering high density population areas (such as a large city or a metropolis),

∙ using ring topologies (or a group of rings, each ring covering a different area, if the population

density requires more capacity),

Regional networks have the same functionalities as the metropolitan networks, but operate in low density

population areas (rural). This results in longer link lengths to collect the same amount of traffic as in

metropolitan case [Par08], and the geographical distribution of population might require the use of other

topologies than rings. Core networks are characterised by [Par08], [Cof02], [Sal99] :

∙ having active elements (using always optical amplification and elements with the highest perfor-

mance in the network),

∙ low granularity (traffic that has been aggregated and groomed in the lower hierarchical layers of

the network),

∙ low variation in traffic flow (result of aggregation),

∙ operating with a more limited number of protocols than metro networks,

∙ transporting traffic over long distances (between big cities, countries and even continents),

∙ using an irregular mesh topology.

The main characteristics of the several layers of the telecommunication network are summarized with

some typical values in table 1.1.

Table 1.1.: Comparison of the characteristics of the several layers of a telecommunication network[Par08], [Sal99], [Lee06] and [Chan08].

Sub- Total Span Aggregation Topologies Bit-rates Protocol Other charac-network distance length factor (typical max.) variety teristics

[km] [km] [Gbps]domestic < 0.1 < 0.1 none almost all < 1 high passive

access < 20 < 20 high almost all < 2.5 high passivemetro < 300 < 80 medium ring 10 medium urban areas

regional < 600 < 80 medium ring and others 10 medium rural areascore < 5000 < 150 low mesh 40 low long distance

6

The aim of this work is to study the characteristics of an optical transport system at core level, being then

of interest to study more deeply the characteristics and challenges of these networks.

1.3.2. Optical core networks characteristics and challenges

Core networks had initially a typical linear or ring topology adapted to the voice traffic (a local, steady

and predictable traffic). But the ever more dominant position of data traffic influenced a change of topol-

ogy, to a irregular mesh topology which best suits the unpredictability, distance intensive and dynamic

characteristic of data traffic [Zys02]. The transport technology used at core level is dense wavelength

division multiplexing (DWDM), using always optical amplification, with channels at 10 Gbps spaced

0.4 nm (channel spacing of 0.2 nm is also possible to find) or channels at 40 Gbps spaced 0.8 nm

[Par08]. The fibre spans can range nowadays from 50 km (submarine systems) up to 240 km (repeater-

less systems) [Zhu02], but typically in terrestrial systems range from 100 km to 120 km [Des06]. Some

optical links use “dispersion matched” fibre spans (in which two fibres with similar characteristics in

dispersion magnitude but with opposite signs are connected in series). However, the high attenuation of

such fibre spans requires a high input power, which results in high nonlinear effects penalty. The current

trend is to use non-zero dispersion shifted fibre (NZDSF) which has a low dispersion coefficient over a

wide band and lower attenuation (in comparison to the dispersion matched solutions) [Ped02], ideal for

ultra long haul (ULH). The trend is that in the future, the network tends more and more to turn from

the traditional hierarchical circuit-based switching network to more distributed networks adapted to data

transmission. The development of optical technology is expected to continue and begin to replace the

electronic in the high frequency part of systems [O’M08]. As a result of this development, functions such

as all-optical regeneration, optical monitoring and optical buffering will in the future enable a further in-

crease in data rates and capacity with reduced power and size of the equipment. These new functions are

the key elements to implement more complex optical switches necessary for more advanced switching

technologies in future optical networks, such as dynamic optical circuit switching, optical burst switch-

ing and optical packet switching [O’M08]. This new equipment will at first however, be deployed only

in the core network, where the number of users by which the cost is split is the highest. The challenges

when designing a core network nowadays are basically three: (a) traffic volume, (b) quality (delay and

errors) and (c) reliability [Nak08]. From these challenges, the one with more interest to this work is the

first. The growth in data traffic demands for an equivalent growth in the capacity of the network that

assures a sufficient margin in case of a traffic peak. This, however, might be technologically challenging

to achieve considering the actual growing rates [Des06].

7

1.4. Optical signals

1.4.1. Optical signals at 100 Gbps

There are several solutions proposed for 100 Gbps channels and these can be divided into two major

groups: serial solutions and parallel solutions. The serial solutions use modulations that rely on one

single data stream and the parallel solutions on several parallel data streams [Ray08]. Some of the serial

solutions proposed are:

∙ on-off keying (OOK) variants such as return to zero (RZ) or non-return to zero (NRZ) [Win05],

vestigial side band (VSB) [Leh07] and duobinary (DB) [Sch06],

∙ phase coded variants, such as differential quadrature phase shift keying (DQPSK) [Win08-Oct]

and polarization multiplexing differential quadrature phase shift keying (PM-DQPSK) [Cha08].

The main advantage of all OOK variants is the low complexity of the transmitter and receiver. However,

these OOK modulations have lower spectral efficiency and are more sensitive to GVD and PMD than the

phase coded variants [Leh07]. The phase coded variants present higher spectral efficiency and require

components with less bandwidth than the OOK modulations [Win08-Oct]. On the other hand, some

parallel solutions proposed are: orthogonal frequency division multiplexing (OFDM) [Jan09] or using

more WDM channels combined with any other existing solution [Win08-Oct], [Ray08]. As mentioned

in subsection 1.2.1, the option of using more WDM channels has been already put aside, leaving OFDM

to be analysed.

OFDM is a multi-carrier modulation scheme, in which frequency-closely-spaced orthogonal sub-carriers

are used to carry parallel low symbol rate streams of data. A high bit rate stream is divided between

the sub-carriers and then each low bit rate stream is transmitted in each sub-carrier using a conventional

modulation [Shi08-Jan]. Examples of such modulations can be quadrature phase-shift keying (QPSK) or

M-order quadrature amplitude modulation (M-QAM) [Jan09]. Due to the large number of sub-carriers,

each sub-carrier occupies a narrowband, which results in greater resilience to fibre dispersion in com-

parison to a serial solution. The main advantages of OFDM are: (1) resilience to dispersive effects,

(2) high spectral efficiency, (3) adaptive transmission rates and (4) fast and efficient (de)modulation

of the OFDM signal by the use of a fast Fourier transform (FFT) algorithm. The main disadvantages

are: (1) sensitivity to nonlinear effects and (2) high peak to average power ratio (PAPR) [Shi08-Jan].

In dynamically reconfigurable networks a precise manual compensation of the dispersion becomes im-

practical, specially with the increase of transmission rates. In addition to the OFDM natural resilience

against these effects, OFDM enables electrical channel compensation in the frequency domain without

8

using complex equalization filters. For these reasons and due to its high spectral efficiency compared

to other OOK modulations, the use of OFDM in optical transmission is and has been investigated and

developed [Shi08-Jan].

1.4.2. Optical OFDM signals

There are two main trends in optical OFDM: the direct detection optical OFDM (DDO-OFDM) and the

coherent optical OFDM (CO-OFDM). In DDO-OFDM, the OFDM signal amplitude is transformed in

optical intensity. The optical carrier is also transmitted so that the detection at the receiver side can be

realized using a simple photodiode. This results in a simplified architecture for the receiver and this

is the advantage of DDO-OFDM in relation to CO-OFDM. But, due to the nonlinearities (both from

the optical fibre as well as from the photodetector), the presence of the optical carrier (strong signal)

generates several N-order intermodulations between the carrier and the signal which results in signal

degradation. These intermodulations can be avoided if a guard band between the OFDM band and the

carrier is inserted. However, this guard band reduces severely the spectral efficiency. Alternatively, the

optical power of the transmitter could be reduced, limiting significantly the reach. For these reasons

the DDO-OFDM is more suitable for short reach or cost-effective applications [Shi08-Jan], [Jan08-Jan].

In CO-OFDM, the I/Q component of the optical field of the laser beam carries the I/Q components of

the OFDM signal, respectively. The result is an optical signal without optical carrier (carrier suppres-

sion). The optical to electrical conversion at the receiver is implemented by coherent detection using a

local oscillator. The advantages of CO-OFDM in comparison to DDO-OFDM are a higher sensitivity

(which improves the reach), better spectral efficiency/reach trade-off (which becomes critical at high

rates) and electrical channel compensation is more effective [Du08]. Concluding, CO-OFDM is better

suited for ULH transmissions than DDO-OFDM, being therefore, the best candidate to achieve 100 Gbps

per channel in ULH.

1.4.3. Trade-offs and limitations in optical OFDM

Some key parameters of an OFDM system are good indicators of some important characteristics of an

optical OFDM transmission system.

FFT size

This parameter equals the number of sub-carriers of an OFDM system and is a very important parameter.

Electronic compensation of the channel is only effective as long as the FFT size is large enough, so that

9

the channel frequency response within the sub-carrier frequency range is practically constant. Since the

effects corrected by the electronic compensation are mostly GVD and PMD, the higher the symbol rate

and/or the longer the transmission distance over optical fibre, the more changes the frequency response

of the channel from one sub-carrier to the next. As a result, in order to achieve an effective channel

compensation, higher FFT sizes are necessary [Jan08-Jan]. However, using higher FFT sizes means

higher electronic requirements, that result in increased system complexity. A proper design of this system

parameter becomes a good indicator of the reach and data rate of the OFDM system. In other words, the

higher the FFT size in an OFDM system, the longer and/or the higher are the bit-rate and the transmission

reach of that system.

Training over-head

The electronic compensation of the channel is achieved from measurements of the channel response at

regular intervals (either in frequency and/or in time). This measurement is done by sending training

information together with the data, observing the changes applied to this training information and cal-

culating the channel frequency response. Usually, it is preferable to send as little training information

as possible, since this increases the systems data throughput. However, this channel compensation tech-

nique works as long as the channel frequency response remains constant until the next measurement takes

place. If this does not happen, the measurement turns to be out of date and the compensation applied

to the data symbols is incorrect. In order to avoid this situation, the training information must be sent

regularly enough. Depending on the desired quality of the channel compensation and on the speed with

which the channel changes its frequency response, the training over-head can be set to higher or lower

values [Jan08-Jan].

Guard interval/cyclic prefix duration

The longer the length of optical fibre over which the optical signal is transmitted and/or the wider the

bandwidth occupied by that optical signal, the higher the amount of dispersion suffered by the signal.

The optical signal is “shielded” from this dispersion by the guard interval (time gap between consecutive

OFDM symbols). The ability to shield the signal from the dispersion is proportional to the guard interval

duration [Jan09]. However, this guard interval is not used for data transmission being of interest to make

it as short as possible. For this reason, the guard interval duration is a good indicator of the transmission

reach/bandwidth of an optical OFDM system. The longer the guard interval/cyclic prefix duration, the

greater the reach/bandwidth of the system.

10

Launched power

It is in the best interest to have the optical launched power (optical power of the signal at the input of

the optical fibre at the transmitter side) as high as possible. However, due to the high PAPR of CO-

OFDM signals, the higher the launched power, the higher are the distortions imposed on the signal due

to fibre nonlinearities. The solution to reduce the effects of the nonlinearities lies in either reducing

the launched power and/or reduce the PAPR of the signal (using techniques such as partial carrier fill-

ing) [Shi08-Jan].

1.5. Objectives and dissertation organization

The main objective of this work is to study the limitations imposed by the ROADMs on the performance

of core networks using CO-OFDM signals at 100 Gbps. This objective is achieved by evaluating the

performance of CO-OFDM systems with and without ROADMs in the transmission link while using a

low enough optical launched power, so that fibre nonlinearities effects can be neglected.

The dissertation is structured as follows.

In chapter 1, the study of core networks and their characteristics, as well as the analysis of the solutions

proposed in the literature for those networks are performed. Based on the advantages of OFDM, it is

studied which type of OFDM signal is best suited to a core network. The objectives and contributions of

the work, as well as the dissertation organization are presented.

In chapter 2, the basics of OFDM signals and the transmission systems used are presented and explained.

The technical assumptions taken in this work are listed, the design of transmission systems is performed

and the used parameters are presented.

In chapter 3, the models of the components used in the optical link are studied and presented. The used

ROADMs are studied and two models are developed. The effects resulting from a chain of these compo-

nents are presented and explained.

In chapter 4, the performance results of the transmission systems are presented. The transmission per-

formances over optical paths with and without ROADMs are compared and the effects of ROADMs on

the performance are discussed. The conclusions of each configuration scheme result are presented.

In chapter 5, the final conclusions of this work and suggestions for future work on this subject are pre-

sented.

11

1.6. Main contributions of this work

In the author’s opinion, the major contributions of this work are:

∙ demonstration of the impact of ROADMs on the performance of CO-OFDM signals,

∙ design of OFDM transmission system,

∙ development of an CO-OFDM simulator in MATLAB,

∙ demonstration of fibre dispersion compensation capacity of CO-OFDM systems,

∙ demonstration of improved performance by using cyclic extension instead of cyclic prefix in CO-

OFDM,

∙ modeling of wavelength selective switches (WSS) and optical filters from experimental data,

∙ demonstration of performance improvement by using polarization division multiplexing with lin-

ear transmission over a real optical link.

12

2. System description

In this chapter, the CO-OFDM transport system used along this work is described. In section 2.1, the

OFDM signal is characterised. In section 2.2, the CO-OFDM transmission system is explained. First the

electrical part of the system is described in subsection 2.2.1 and then the optical part in subsection 2.2.2.

The complete CO-OFDM system is presented in subsection 2.2.3. The technical assumptions made in

this work are presented in subsection 2.2.4 and the parameters chosen for the system in simulated in this

work are presented in subsection 2.2.5.

2.1. OFDM signals

2.1.1. Basics of OFDM signals

As referred in subsection 1.4.1, OFDM is a special multi-carrier modulation (MCM), in which its Nsc

sub-carriers are orthogonal between themselves [Shi08-Jan]. The MCM concept works as follows:

∙ the main high rate stream of data is divided into Nsc parallel low rate streams,

∙ each low rate stream is transmitted in each sub-carrier,

∙ at the receiver side, the data is recovered from the sub-carriers and the high rate data stream is

recovered.

In OFDM, the sub-carriers use simple modulation formats such as quadrature phase-shift keying (QPSK)

or M-ary quadrature amplitude modulation (M-QAM). Each sub-carrier transmits one symbol using the

selected format during one OFDM symbol. One OFDM symbol results from the superposition of all the

sub-carriers, which in the time domain looks just like noise, being then more interesting to observe the

spectrum instead (see figure 2.1). Each OFDM symbol has the duration of Ts seconds. The description

of an OFDM signal, s(t), in time is given by

s(t) =+∞

∑i=−∞

Nsc−1

∑k=0

ci,k ⋅ e j2π⋅ fk⋅(t−i⋅Ts)H(t) ⋅H(i ⋅Ts− t) (2.1)

13

where c(k, i) is the data symbol at the kth sub-carrier on the ith OFDM symbol, fk is the frequency of the

sub-carrier number k (see equation A.3), t is time in seconds and H(x) represents the Heaviside function

[Shi08-Jan]. The orthogonality of the sub-carriers is guaranteed as long as the frequency spacing, ∆ f ,

Figure 2.1.: OFDM signal in time domain (left) and in frequency domain (right). The OFDM signalpresented here has a data rate of 56 Gbps, its OFDM symbol duration is 38.3 ns and uses 16-QAM onthe sub-carriers. For more information on other characteristics, consult table 2.1 under system no. 2.

between them is a multiple of the inverse of the OFDM symbol duration [Shi08-Jan], given by

∆ f = m ⋅ 1Ts, m ∈ ℕ+ (2.2)

Despite strong spectral overlapping by the orthogonal sub-carriers of the OFDM signal, the information

carried by each sub-carrier can be recovered without inter-carrier interference (ICI). This is the main

reason, leading to the high spectral efficiency of OFDM referred in subsection 1.4.1. The first approach

to generate a MCM signal is using a bank of oscillators, mixers and filters at both transmit and receive

end [Shi08-Jan]. However, the OFDM modulation/demodulation can be implemented using the inverse

discrete Fourier transform (IDFT)/discrete Fourier transform (DFT) respectively and overcoming this

way the complexity of the first approach [Wei71].

2.1.2. General concepts for OFDM transmission

OFDM stream

OFDM transmissions are realized in OFDM streams and a OFDM stream is constituted by OFDM

frames. Each OFDM frame is a series of OFDM symbols. In order for an OFDM stream transmis-

sion to work, the transmission system has to be able to compensate the transmissions effects that distort

the signal (such as fibre distortion and phase-shifts due to synchronism errors). For this the system

must regularly measure the transmission channel. There are two techniques to do this: either send-

14

ing pilot sub-carriers (PS) [Ma08] or sending training symbols (TS) [Shi08-Jan]. Both techniques rely

on sending training data on predefined sub-carriers/instants, so that the receiver is able to measure the

channel frequency response on these sub-carriers/instants. Once the frequency response on these sub-

carriers/instants is known, the frequency response for the other sub-carriers/instants is interpolated to

estimate the complete channel frequency response H(k, i). The difference between PS and TS is that, in

PS the pilots are sent together with data carrying sub-carriers in the same OFDM symbol and in TS a

whole symbol is completely filled with training pilots where no data is sent [Shi08-Jan]. In this work,

it was chosen to use TS, among other reasons, because of the synchronisation algorithm used (see sec-

tion A.7 in appendix A). The OFDM frame used in this work begins with an OFDM training symbol,

being then followed by Nsp OFDM data symbols (DS). A scheme of the OFDM stream is shown in figure

2.2.

Figure 2.2.: Scheme of the OFDM stream used in this work. Each OFDM frame consists in a series ofOFDM symbols, which the first is a training symbol (TS) and the remaining Nsp are data symbols(DS).

Cyclic prefix

In an OFDM transmission, each OFDM symbol is separated by a guard interval Gi, where no signal is

transmitted. However, in a transmission over a dispersive channel, the energy of each OFDM symbol

spreads to the guard interval before and after (this effect can be seen in annex A1). If the delay spread

of the channel, td , is equal or greater than the guard interval Gi, this results in inter-symbol interference

(ISI), what must be avoided at all cost if the a good system performance is to be achieved [Shi08-Jan].

For td greater than zero, the distortion caused to the signal exists (see appendix F) and has to be corrected.

This correction can be achieved in OFDM by filling the guard interval with a portion of signal, copied

from the OFDM symbol signal [Shi08-Jan]. Figure 2.3, shows the difference between cyclic prefix (CP),

cyclic postfix (CPF) and cyclic extension (CE). If the signal portion is copied from the OFDM symbol

following the guard interval, then the signal filling the interval is called CP [Kim06]. If the signal portion

is copied from the OFDM symbol preceding the guard interval, then the signal filling the interval is called

CPF. If both CP and CPF are used simultaneously, then the signal portion filling the guard interval has

15

been referred in the literature as CE [Djo09]. At the receiver side, after the propagation through the

dispersive channel, the guard interval (containing the CP, CPF or CE) is cut out and the OFDM symbol

is extracted and passed to the DFT for demodulation.

As a result of channel dispersion, the complete distorted OFDM symbol is longer than the fast Fourier

transform (FFT) window. However, thanks to the copied signal portion (CP or CPF), the end of the

extracted signal has continuity with its beginning. As a result, the extracted signal can be seen as one

period of a periodic signal, which FFT can be calculated from one single period. The received data

symbols, y(k, i) can be extracted from the output of the FFT. These data symbols are related to the

transmitted data symbols, c(k, i), by the transmission channel transfer function as given by

y(k, i) = H(k, i) ⋅ c(k, i). (2.3)

It is important to notice that, the signal periodicity or signal continuity condition is maintained also when

using CE. For this reason, the equation 2.3 is also valid for that case.

Figure 2.3.: Examples of OFDM systems using: cyclic prefix (first row), cyclic postfix (second row) andcyclic extension (third row).

16

General calculations

The bandwidth of an OFDM signal, Bo f dm, is given by the sub-carrier spacing, ∆ f , multiplied by the

number of sub-carriers used, Nu (see oversampling in section A.2), as expressed by

Bo f dm = ∆ f ⋅Nu. (2.4)

The bit rate of an OFDM signal, Db, is the number of bits transmitted over the time of transmission and

is given by

Db =Nsp

Nsp +1⋅ Nu ⋅Nb

Ts +Gi. (2.5)

where Nb is the number of bits transmitted on each sub-carrier. As referred before: Gi, Ts and Nsp are the

guard interval duration, OFDM symbol duration and number of OFDM data symbols between two TS,

respectively. Considering the ratio of used sub-carriers to be su and the ratio between Gi and Ts to be cTs ,

then equation 2.5 can be rewritten as

Db =Nsp

Nsp +1⋅ su ⋅Nsc ⋅Nb

Ts ⋅ (1+ cTs). (2.6)

In order to maintain/achieve a certain Db, the value of Ts can be derived from 2.6 and given by

Ts =Nsp

Nsp +1⋅ su ⋅Nsc ⋅Nb

Db ⋅ (1+ cTs). (2.7)

Replacing equation 2.7 in equation 2.2, Bo f dm is given by

Bo f dm = m ⋅Nsp +1

Nsp⋅ Db

Nb⋅ (1+ cTs), m ∈ ℕ+. (2.8)

The spectral efficiency of a OFDM system is given by the bit rate over the bandwidth of the signal. The

spectral efficiency, Se, is obtained by

Se =Db

Bo f dm=

1m⋅

Nsp

Nsp +1⋅ Nb

(1+ cTs), m ∈ ℕ+. (2.9)

2.2. CO-OFDM transmission system

A CO-OFDM transmission system requires naturally CO-OFDM transmitters and receivers. These are

built of OFDM coders/decoders and coherent optical transmitters/receivers. These elements will now be

presented.

17

2.2.1. OFDM signal coder and decoder

The structures of the OFDM coder and decoder implemented in the simulator used in this work are

presented in figure 2.4 and figure 2.5 respectively. The OFDM signal is built at the coder as follows:

Figure 2.4.: Scheme of the OFDM coder, where CP is a cyclic prefix module.

1. the input bit stream is split in Nu parallel bit streams, one for each sub-carrier, by the serial-to-

parallel converter (S/P),

2. each of the parallel bit streams is converted into a data symbol at the constellation mapper,

3. each data symbol is passed through the pre-emphasiser,

4. the Nu pre-emphasised symbols together with some zeros (in order to generate the oversampling

mentioned in appendix A.2.1) are fed to the input buffer of the IFFT+P/S module (IFFT window

of size Nsc) which calculates the IFFT of the array present at the input buffer and converts the

result (a vertical array) into a serial stream of samples which is the OFDM symbol signal with the

parallel-to-serial converter (P/S),

5. the OFDM symbol signal receives the CP/CPF/CE at the cyclic prefix module (CP-module) and

becomes a complete OFDM symbol signal, in the end of the CP-module the real (Re) and imaginary

(Im) parts of the complete OFDM signal are split,

6. the two parts of the complete OFDM symbol signal are then converted to an analogic signal by the

sample and hold (SH),

18

7. finally the low-pass filter (LPF) attenuates the aliasing products (see appendix A.2.1) generated by

the digital to analog conversion process.

The output of the OFDM coder are two signals (I and Q), one carrying the real part of the OFDM symbol

signal and another carrying the imaginary part. These two outputs will then be combined in one single

signal as in-phase and quadrature components.

Figure 2.5.: Scheme of the OFDM decoder

At the OFDM decoder the information bits are retrieved from the OFDM signal as follows:

1. the I and Q components of the received signal are filtered by a LPF to reduce the channel noise

power,

2. both the I and Q filtered signals are then sampled by a analogic-to-digital converter (ADC),

3. the beginning of each OFDM symbol is detected by a symbol synchronism unit and these time

instants are signalled to the control unit which operates the two switches after the delays,

4. the control unit based on the symbol beginning instants, on the symbol duration and on the delay

introduced to the signal (which compensates for the synchronism unit processing time), cuts off

the CP/CPF/CE from the I and Q signals,

5. the remaining samples of Q are multiplied by j and are added to the remaining samples of I, the

resulting complex signal is fed to the input of the S/P+FFT module,

19

6. the S/P+FFT module converts the serial signal into a parallel one and calculates the FFT of the

last, the result of the FFT contains the complex values of each sub-carrier,

7. the complex values of the sub-carriers used for oversampling are dropped and the complex values

of the remaining sub-carriers are passed to the equalizer,

8. the equalizer, based on the distortion measured on the previous received training symbol, applies

the inverse transfer function in order to reduce the distortion and recover the complex values sent

by the transmitter,

9. the complex values returned by the equaliser are fed to the symbol detectors that determine which

symbol was sent and return the corresponding set of bits,

10. these bits are then used by the P/S to build the output bit stream.

The elements and modules used in the OFDM coder and decoder are explained in more detail in ap-

pendix A.

2.2.2. Coherent optical transmitter and receiver

The optical part of the CO-OFDM system requires optical coherent transmitters/receivers. The schemes

of the coherent optical transmitter and receiver used are presented in figures 2.6 and 2.7, respectively.

The coherent optical transmitter works by modulating the in-phase and quadrature components of the

Figure 2.6.: Scheme of the coherent optical transmitter (CO-TX). The LD1 represents lase diode. TheMach-Zehnder modulator (MZM) is an optical modulator. The -90o block is a device that introducesa -90 degree phase-shift to the optical signal.

optical signal generated by LD1 according to the electrical input signals Ich and Qch, respectively. This

is achieved by:

1. splitting the optical signal generated by LD1 in two identical signals,

20

2. modulating each of these signals with the electrical input signals Ich and Qch, using for that the two

Mach-Zehnder modulators (MZM),

3. introducing a phase-shift of 90o in one of the modulated optical signals (in this case the signal

carrying electrical signal Qch),

4. adding the result in one optical signal.

Figure 2.7.: Scheme of the coherent optical receiver (CO-RX). The OF represents an optical filter, theLD2 represents a tunable optical source (typically a laser) and the PIN photo-diode are used as pho-todetectors.

The receiver has the task of recovering the in-phase and quadrature components from the received optical

signal. Assuming that the optical source at the receiver is already synchronised with the optical signal

received, the recovery process is achieved by:

1. splitting the received signal in two identical signals and adding a phase-shift of 90o (done by the

3-dB coupler, see appendix B) to one of them,

2. splitting the local optical signal (LD2) in two identical signals and adding a phase-shift of 90o to

one of them as well,

3. combining these four signals and obtaining the photocurrent of each of the combined signals,

4. processing the photocurrents and extract the electrical signals Ich and Qch.

The extended analysis of the coherent transmitter and receiver is presented in appendix B.

21

2.2.3. CO-OFDM transmitter and receiver

In this subsection the complete CO-OFDM system is presented. As in order to transmit one single OFDM

signal at 112 Gbps requires a higher electronic complexity (see subsection 2.2.5) an alternative system

variant using polarization division multiplexing (PDM) is also considered. The first variant using one

single OFDM stream to carry all the data is named system no. 1 and system 2 makes use of PDM to carry

one OFDM stream on each polarization direction. The advantage of system 2 is that the data rate of each

OFDM stream is half (two polarization directions) of the data rate of system 1. This reduction of data

rate makes each stream more resilient to fibre dispersion (enabling system 2 under the same conditions

to reach longer distances than system 1) and lowers the requirements on the electronic complexity of the

OFDM coder and decoder. The schemes of system no. 1 and 2 are presented in figure 2.8

Figure 2.8.: Scheme of system 1 (first row) transmitting one single data stream at Db and scheme 2 (sec-ond row) transmitting two data streams at 0.5 ⋅Db using PDM. The PDM is implemented by usinga polarization multiplexer (PM) at the transmitter side and a polarization demultiplexer (PD) at thereceiver side.

2.2.4. Technical assumptions

In order to simplify the achievement of the objectives of this work some technical assumptions were

made:

∙ the lasers used as optical sources are ideal, meaning the optical signal they generate:

1. has constant output power (no noise in amplitude),

2. has constant phase (no phase noise),

22

3. has constant frequency (no frequency drift),

∙ the synchronism of the system is perfect, namely:

1. the I and Q channels have the same time delay resulting from being transmitted on the same

optical signal,

2. the laser at the receiver is perfectly synchronised with the phase and frequency of the re-

ceived signal,

3. the two polarizations suffer from the same time delay,

4. the clock generators at the transmitter and receiver are ideal and do not drift,

∙ the polarization multiplexer (PM) and the polarization demultiplexer (PD) are ideal, meaning:

1. they do not suffer from polarization dependent losses (PDL),

2. they separate perfectly the two polarization directions

∙ the only source of noise considered is optical, because a long number of erbium doped fibre am-

plifiers (EDFAs), more than 10, is used in ultra long haul (ULH) and the electrical noise is kept

low to increase reach,

∙ the noise does not affect the measurement by the CO-OFDM receiver of the channel frequency

response and therefore does not cause any errors due to incorrect equalization,

∙ the noise power splits evenly over the two polarization directions and evenly over the in-phase and

quadrature components of the optical signal,

∙ there exists a digital signal processor (DSP) that can calculate an FFT with the size and in the time

required to achieve the data rates mentioned in this work,1

∙ no polarizers are used in the systems simulated in this work,

∙ the transmission channel has a linear behaviour.

2.2.5. Technical parameters of the CO-OFDM system

The design of the system is done in three main steps:

1The experiments mentioned in the literature at such high data rates generated the OFDM signal offline. The OFDM signalwas then loaded on to an arbitrary waveform generator (AWG) and the received OFDM signal was sampled and savedbefore being processed offline.

23

1. knowing the desired bit rate and the maximum bandwidth the OFDM signal may occupy, from

equation 2.4 it is retrieved which modulation must be used on the sub-carriers (for several values

of cTs),

2. imposing the maximum transmission reach (Lkm) in equation C.1 and knowing the bandwidth of

the OFDM signal, the duration of the guard interval is obtained,

3. using the value of the guard interval in equation 2.7, the values that must be used for the FFT size

and cTs are obtained.

The major requirements imposed on the system are a bit rate of 112 Gbps and a transmission reach

greater than 1000 km. The extended design of the system parameters is done in appendix C and the

obtained system parameters are summarized here for convenience.

Table 2.1.: Parameters of the two system variants, no. 1 and no.2. *Note that the OFDM signal bandwidthis in base band. For more information, refer to appendix C.

Data rate/ No. of No. of used SymbolSystem no. OFDM stream sub-carriers sub-carriers duration

Db [Gbps] Nsc Nu Ts [ns]1 112 4096 2459 76.7

2 56 1024 615 38.3

CP Bandwidth/ OF -System no. duration OFDM stream bandwidth -

[ns] Bo f dm [GHz]* [GHz] -1 7.7 16 35 -

2 3.8 8 17.5 -

In common, the two systems have the modulation used in the sub-carriers (16-QAM), the number of

OFDM data symbols per OFDM frame (25 data symbols) and do not have forward error correction

(FEC) implemented.

2.3. Conclusions

Two transmission systems have been described and designed in this chapter (system no. 1 and system

no. 2). System no. 1 transmits one single OFDM stream at 112 Gbps. System no. 2 transmits two

OFDM streams at 56 Gbps and occupies half the bandwidth used by system no. 1 by using PDM and

transmitting each stream in a different polarization. On one hand, the use of PDM represents an increase

of the complexity of the transmission system, but on the other hand, the technology to implement PDM

is already available [Jan09] and the electronics needed to process a stream at 56 Gbps are easier to

24

implement than the ones needed to work at 112 Gbps. In addition, system no. 2 employs less sub-

carriers than system no. 1, what simplifies the OFDM coder and decoder.

As for what concerns the transmission through a chain of ROADMs, the reduced bandwidth of the optical

signal of system no. 2 is an advantage in comparison to the signal of system no. 1.

25

26

3. Description of in-line components

In this chapter, the components used between the transmitter and the receiver are presented and modeled.

In section 3.1, the optical fibre used in this work is presented. In section 3.2, the used optical amplifiers

(erbium doped fibre amplifiers-EDFA) and its model are presented. In section 3.3, the reconfigurable

optical add-drop multiplexer (ROADM) and the used wavelength-selective switches (WSS) are presented

and modeled. In section 3.4, the effects of a chain of ROADMs and EDFAs are presented and studied.

3.1. Optical fibre

Over the years, several types of optical fibres have been developed, from the very first standard fibre up

to many others such as the dispersion-shifted, dispersion flattened and dispersion compensating fibres.

In order to keep the results obtained from this work comparable to what has been published in the

literature, it has been chosen to use the same type of fibre that is commonly used in the publications

[Jan08-Jan],[Jan09],[Shi07] namely standard single mode fibre (SSMF). As mentioned in section 2.2.4,

it is assumed that the transmission fibre has a linear behaviour. This means that no fibre nonlinear effects

(such as self-phase modulation, cross-phase modulation and four-wave mixing) are considered. The

only effects taken into consideration are attenuation (due to fibre losses) and group velocity dispersion

(GVD) [Agr1].

The dispersion broadens the signal impulses, by spreading the signal energy over time (this can be seen

in figure F.1 in appendix F). As a result the broadened pulses that compose the signal start to interfere

with each other. If the interference on given points is destructive, the signal is attenuated on those points

and this energy is lost. Thus, the total signal power is reduced. Another fibre effect are the fibre losses.

The losses reduce the signal energy and the whole signal is attenuated. Altogether, the model of the fibre

is then given by

H f ib(ν) = 10−αdB(ν)⋅Lspan

20 ⋅ e− j⋅Lspan⋅1000⋅β (2π⋅ν), (3.1)

where αdB(ν) is the fibre losses in dB/km, Lspan is the length of the fibre span in km (which are then con-

verted to metres by the multiplication by 1000), ν is the optical frequency in Hz and β is the propagation

27

constant in the fibre in rad/m.

Although the value of αdB depends of the optical frequency, the value of αdB varies less than 0.05 dB/km

within the entire C-band (which is approximately 4400 GHz wide) [Agr1]. Since the bandwidth of

signals used in this work is much smaller than that (< 50 GHz), it is considered that the fibre losses are

independent of the frequency.

The pulse broadening results from the frequency dependency of β . In general, the exact expression of

β is not known [Agr1]. For this reason, it is useful to expand β in a Taylor series around the carrier

frequency ν0 given by

β (∆ω) = β0 +β1 ⋅∆ω +β2

2⋅∆ω

2 +β3

6⋅∆ω

3. (3.2)

where ∆ω is given by

∆ω = 2 ⋅π ⋅ (ν−ν0). (3.3)

The first two terms (β0 and β1) in equation 3.2 account for the propagation constant at frequency ν0 and

the propagation delay respectively. These effects do not apply any temporal broadening of the impulses

to the signal, being then of little interest for this work. For this reason, β0 and β1 are neglected in the rest

of the work.

The β2 and β3 parameters account for the fibre dispersion of first and second order, respectively.

The β2 term in equation 3.2 is related to the dispersion parameter of the fibre, Dλ , and is given by

β2 =−Dλ ⋅λ 2

02πsl

⋅10−6, (3.4)

where λ0 is the wavelength corresponding to the central frequency of the OFDM band (ν0) in metres, sl

is the speed of light in vacuum in m/s and the parameter Dλ is introduced in ps/nm/km [Agr1]. The β3

parameter is related to the dispersion slope of the fibre, S, which is given by

β3 = 10−3 ⋅S ⋅λ 4

0(2πsl)2 −

λ 20

2πsl⋅β2, (3.5)

where S is introduced in ps/nm2/km [Agr1].

The model of the optical fibre is then given by

H f ib(ν) = 10−αdB⋅Lspan

20 ⋅ e− j⋅Lspan⋅1000⋅(

β22 ⋅(2⋅π⋅(ν−ν0))

2+β36 ⋅(2⋅π⋅(ν−ν0))

3). (3.6)

The values of the parameters αdB, Dλ and S vary between the several types of fibres and depend also on

the used wavelength. A SSMF has typically αdB = 0.2 dB/km, Dλ = 16 ps/nm/km and S = 0.09 ps/nm2/km

at λ0 = 1550 nm. This wavelength is in the C band, commonly used on ultra long haul (ULH) [Agr1].

28

These values are used in the model of the optical fibre except for αdB which is set at 0.25 dB/km to

account for additional losses due to spliters and connectors.

3.2. Optical amplifiers

Any ULH system requires the use of optical amplifiers to compensate for the fibre losses. Such amplifiers

are commonly fibre-based, in which a length of optical fibre is doped with a rare-earth element to provide

the optical gain. The amplification is achieved through an absorption and stimulated emission mechanism

of the rare-earth ions. For this reason, the used rare-earth element determines the wavelength at which the

amplifier operates [Agr3]. EDFAs operate in the wavelength region near 1550 nm, which corresponds to

the C-band [Agr3] and are for that reason used in this work.

The EDFAs need to have a gain which compensates for the losses of the preceding fibre span and optical

components. The gain of an EDFA can achieve 30 dB (or even higher). This imposes a maximum

fibre span length of more than 120 km (for αdB = 0.25 dB/km). However, due to amplified spontaneous

emission (ASE), the EDFA adds noise to the signal during the amplification, degrading the optical signal

to noise ratio (OSNR). This degradation is quantified through the amplifier noise figure, Fn, which is

given by [Agr3]

Fn =SNRin

SNRout= 2 ⋅nsp ⋅ (1−

1ged f a

)+1

ged f a(3.7)

where nsp is the spontaneous emission factor (or population-inversion factor) and ged f a is the gain of the

EDFA in linear units [Agr3]. Equation 3.7 shows that Fn grows with the gain ged f a. Therefore, EDFAs

with a higher gain (needed for longer fibre spans) add more noise to the signal. This is just one of a

number of factors that influences the choice of the length of the fibre spans used in an optical link. Other

factors are:

∙ economical, the length of the fibre spans, determines the number of EDFAs used and influences

the costs of the optical link,

∙ geographical, the distance between the points of traffic extraction (and therefore of the optical

links) is imposed by the geography of the terrain what ultimately has an impact on the length and

number of fibre spans used.

The optimisation of the length of the fibre spans is beyond the objectives of this work. For this reason, a

typical value for the length of the fibre span in ULH is used (Lspan = 80 km).

29

It is referred in section 3.1 that the optical fibre used has 0.25 dB of losses per each km of fibre. For an

80 km span, this results in 20 dB of fibre attenuation. As a consequence, the EDFA at the end of each

fibre span is designed to compensate for 20 dB of fibre attenuation with 20 dB of gain.

The spectral density of the ASE noise, per polarization direction, generated by each EDFA is given by

Ssp(ν0) = nsp ⋅ (ged f a−1) ⋅h ⋅ν0, (3.8)

where h is the Planck constant [Agr3]. By replacing equation 3.7 in equation 3.8 and multiplying it by

the reference bandwidth Bre f (see section D.2.2 in appendix D), the noise power added by one EDFA in

each polarization direction Pn−ed f a, is obtained

Pn−ed f a(ν0) =12⋅ (Fn ⋅ged f a−1) ⋅h ⋅ν0 ⋅Bre f , (3.9)

3.3. ROADM

A ROADM is a complex device with several possible different configurations. However, it is not within

the scope of this work to explain these devices in detail, but instead to analyse their impact on the

performance of an CO-OFDM transmission system. In order to do so, it is first necessary to understand

the basic operation of a ROADM. A simplified layout of a ROADM is shown in figure 3.1. As it can

be seen in figure 3.1, one fundamental component of the ROADM is the WSS (since it is responsible for

the selection of the wavelengths that are added/dropped).

Due to the objective of this work, only the optical filtering effect of the WSS is considered. Since each

optical signal that crosses a ROADM (independently of whether this signal is extracted from its originary

light-path, λ3 in figure 3.1, or passed/expressed through the ROADM, λ1 and λ2 in figure 3.1) it passes

through exactly one WSS (see figure 3.1), the ROADM can be replaced by one single WSS. As a result,

each ROADM is reduced to its WSS.

3.3.1. Wavelength selective switch

A WSS is a dynamic configurable bi-directional optical device, that has M selectable optical ports and

one single common optical port as shown in figure 3.2. Depending on the transmission direction (from

selectable port to common port or vice-versa), the WSS is defined as an Mx1 WSS or as an 1xM WSS,

respectively. Each wavelength/channel present at the common port can be connected to one, and only

one, of the M selectable ports. Ideally, there is no intra-channel cross-talk and the same wavelength

30

coming from any of the other selectable ports is blocked to reach the common port.

As to the switching, no extensive explanation will be here added besides referring that the most used

optical switching technologies for WSSs are [JDSU]:

Figure 3.1.: Simplified scheme of a three-degree (3 line pairs: East,West and South) ROADM, using powersplitters, WSSs and optical amplifiers (OA). Many other devices, such as performance monitors, gaincontrol units and control modules, are needed to complete the ROADM [Feu08]. However, thesedevices are not represented for simplicity. The example presented shows how the optical signal atwavelength λ3 coming from the West is deviated to South, while the other two wavelengths (λ1 andλ2) are passed/expressed through the ROADM in the West-East light-path.

(a) (b)

Figure 3.2.: Ideal WSS, working on both directions, from selectable ports to common port (3.2a) andvice-versa (3.2b). The wavelength selection is perfect, so that no channel cross-talk exists. Thismeans when a given channel from a given selectable port is selected to be present at the common port,that same wavelength at all other selectable ports is blocked to reach the common port.

31

∙ micro-electro-mechanical (MEM) technology ,

∙ liquid-crystal (LC) technology.

For more details on MEM technology consult [Agr913] and on LC technology consult [JDSU][Agr914].

3.3.2. WSS - simplified model

In this work, a WSS 8x1 from the Oclaro company is used. It can switch 80 wavelength division multi-

plexing (WDM) channels, each channel occupying a 50 GHz bandwidth. In order to obtain experimen-

tally the transfer function of the WSS, ASE noise is fed to the common port of the WSS while all the

channels are routed to the same selectable port, where an optical spectrum analyser (OSA) is connected.

The obtained power spectral density (PSD) is then divided by the PSD of the noise floor at the input and

the WSS transfer function is obtained. This transfer function is shown in figure 3.3.

Figure 3.3.: Transfer function of all WDM channels overlapped. This graphic was retrieved experimen-tally from the WSS.

The transfer function of one WDM channel is needed for this work. This could be obtained in a second

experiment using the same method, if all WDM channels but one were blocked. Unfortunately, it was

not possible to obtain the graphic of this second experiment from the owners of the WSS. However, some

extra information about the transfer function of the WSS was supplied:

∙ the attenuation of the WSS outside the pass-band of one WDM channel is 45 dB higher than within

the pass-band,

32

∙ the transfer function of each single WDM channel does not change from one channel to the other

(the transfer function is the same for all channels, centred at the respective channel central fre-

quency),

∙ the transfer function of one single WDM channel can be accuratelly modeled in the pass and

transition bands using a super-Gaussian function.

In order to obtain the equation for the model of the WSS it is first necessary to present the equation of a

super-Gaussian function, which is given by

Hg( f ) = e−ln(√

2)⋅∣∣∣∣ f

fc

∣∣∣∣2⋅ng

, (3.10)

where ng is the order of the super-Gaussian function and fc is the 3-dB cut-off frequency. This equation is

adapted, so that the transfer function of the super-Gaussian band-pass filter (BPF) is obtained and given

by

Hg(ν) = Hg−0 ⋅ e−ln(√

2)⋅∣∣∣∣ν−ν0

νc

∣∣∣∣2⋅ng

, (3.11)

where νc is half of the 3-dB bandwidth of the filter and Hg−0 is the gain of the WSS at the middle of the

channel.

The next step consists in finding the values for the parameters of the filter (νc, ng and Hg−0). The

experimental data indicates that the bandwidth of the filter is around 44 GHz and that its in-band gain

is near -4.3 dB. A fine tuning was conducted until the best match between the WSS model and the

experimental data is obtained for νc = 21.5 GHz, ng = 6 and Hg−0 = 10−4.3

20 .

However, equation 3.11 only describes the behaviour of the transfer function within a 45 dB bandwidth.

Outside this band, the attenuation remains constant at 48.3 dB = 4.3 + 45 dB (as mentioned before in

this subsection). The complete transfer function of the modeled WSS, 20 ⋅ log(Hg(ν)), is plotted over the

experimental data in figure 3.4.

3.3.3. WSS - model with dispersion

A second model for the WSS is also used in this work. This second model is similar to the first but

additionally takes in consideration that the WSS inserts group velocity dispersion (GVD) in the optical

signal (similar to an optical fibre).

The dispersion effect is added to the model of the WSS presented in section 3.3.2 by using the second

term of equation 3.6. The resulting equation for the WSS transfer function within the 45 dB bandwidth

33

Figure 3.4.: Transfer function of the modeled WSS. The transfer function of the experimental WSS (onechannel) is also plotted for comparison.

is given by

Hg(ν) = Hg−0 ⋅ e−ln(√

2)⋅∣∣∣∣ν−ν0

νc

∣∣∣∣2⋅ng

⋅ e− j⋅β (2π⋅∆ν) (3.12)

and Dλ ⋅Lspan = 20 ps/nm and S = 0 ps/nm2/km are considered in β (ω).

3.4. Effects of a chain of ROADMs

Although, in real optical links, ROADMs are only placed at traffic extraction/switching points, in this

work one ROADM is placed at the end of each fibre span. The reason for this is to maximize the number

of ROADMs used in one optical link, so that the effects of a ROADM chain are also maximized. In case

of a chain of ROADMs, the equivalent transfer function presents a narrower bandwidth than one isolated

ROADM. This effect is shown in figure 3.5. The bandwidth narrowing is shown in table 3.1.

It can be seen in table 3.1 that, for system no. 1 (for which the OFDM signal base-band bandwidth is

Table 3.1.: Bandwidth narrowing in a chain of ROADMs.number of ROADMs 1 10 25 40

bandwidth (1-dB) [GHz] 38.7 32.0 29.6 28.5

bandwidth (3-dB) [GHz] 42.5 35.1 32.5 31.2

attenuation at 8 GHz (system no. 2) [dB] ≈ 0 ≈ 0 ≈ 0 ≈ 0

attenuation at 16 GHz (system no. 1) [dB] 0.1 1.0 2.5 4.0

16 GHz, see table C.3) the signal degradation grows beyond 1 dB after 10 ROADMs. For system no. 2

34

Figure 3.5.: Transfer function of a chain of ROADMs for one WDM channel. The gain of the WSSwithin the pass-band was not taken into account. The reason for this, is that the gain of each WSS iscompensated by the optical amplifiers (shown in figure 3.1). It is also assumed that the WDM channelsof all ROADMs are properly syntonised.

(which OFDM signal base-band bandwidth is 8 GHz, see table C.3) however, no signal degradation is

expected.

Figure 3.6 shows that the noise power increases linearly along the number of ROADMs. This makes

Figure 3.6.: Noise power evolution along the line, with and without WSSs. The used EDFA present anoise factor of 5 dB and a gain of 24.4 dB (20 dB for the optical fibre losses and 4.4 dB for the lossesof the WSS). The WSS had one single WDM channel activated and the noise power is calculated inthe reference bandwidth (see section D.2 in appendix D).

sense, since each EDFA adds noise with the same power at the end of the corresponding fibre span. When

WSSs are used, the WSS introduces losses which must be compensated for by the EDFA. This increase

of the gain results in an increase of the noise added at each fibre span. For this reason, the noise power

35

grows faster along the line in comparison to the case where no WSS are used.

3.5. Conclusions

In this chapter, the components used in the optical link are described as well as the effects resulting from

a chain of those components. The two effects resulting from the chain of ROADMs are the narrowing of

the bandwidth (comparatively to one single ROADM) and an increase of the noise power added at each

fibre span.

For system no. 2, the impact of the chain of ROADMs due to the bandwidth reduction is virtually null.

The same does not happen for system no. 1, which after 40 fibre spans has already an attenuation of 4 dB

at the high frequency sub-carriers.

The OSNR value along the line decays faster when ROADMs are used. This means the use of ROADMs

shortens the maximum transmission distance of both systems.

36

4. Results and discussion

In this chapter, the results obtained through numerical simulation are presented. The performances of

the two CO-OFDM system variants, no. 1 and no. 2, for a given OSNR value (section 4.1) and in a real

optical link (section 4.2) are presented. System no. 1 transmits one single full rate OFDM stream and

system no. 2 transmits two half rate OFDM streams, each on one polarization direction.

4.1. System performance for a given OSNR (using a noise loader)

4.1.1. System without ROADMs

The first step consists in finding the optical signal-to-noise-ratio (OSNR) that results in the same perfor-

mance on both systems (no. 1 and no. 2) in back-to-back configuration (using a noise loader to generate

the noise). The target bit error ratio (BER) for back-to-back is 10−4. However, it is observed that a BER

of 1.1 ⋅ 10−4 is obtained in system no. 1 for an OSNR of 19.5 dB and in system no. 2 for an OSNR of

19.6 dB. The obtained BER values were considered acceptable and were used in the simulation of the two

systems at several lengths of standard single mode fibre (SSMF). The results are shown in figure 4.1.

Figure 4.1.: Performance of systems no. 1 (OSNR = 19.5 dB) and no. 2 (OSNR = 19.6 dB) withoutROADMs.

37

Figure 4.1 shows that the performance of the two systems for approximately the same OSNR (existing

a 0.1 dB difference) is virtually equal and constant until the designed maximum reach. This shows that

both transmission systems are capable of compensating for the group velocity distortion (GVD) added

by the SSMF until the designed maximum SSMF length. Figure 4.1 also shows that beyond the designed

maximum reach the performance of both systems starts to degrade visibly (the greater the SSMF length

the greater the performance degradation). Beyond the designed maximum reach, the delay spread of

the channel, td , exceeds the guard interval duration, Gi, inter-symbol interference (ISI) occurs and the

equalizer is no longer able to compensate for the dispersion, leading to bit errors. This increase on

the BER (and therefore performance reduction) would occur at exactly the same SSMF length if both

systems were designed exactly for the same maximum reach. The different SSMF lengths at which

that BER increase occur on each system indicates that the respective maximum reach is not exactly the

same. The design difference can be due to errors resulting from rounding parameters (e.g. a difference of

0.1 ns in Gi in equation C.1 results in approximately a 49 km difference for system no. 2). Nevertheless,

the performance of both systems, shown in figure 4.1, is considered similar enough. However, if the

performance differences between the two systems were to be further reduced, a finer parameter tuning

(of Gi, see appendix C and OSNR) would be required.

4.1.2. System with ROADMs

The BER curves obtained in the previous subsection, where no ROADMs were used in the transmission,

represent the performance reference for each system. The simulations are now repeated under the same

OSNR conditions (19.5 dB for system no. 1 and 19.6 dB for system no. 2), with the difference that a

ROADM is inserted at the end of each fibre span (every 80 km, see section 3.2). Furthermore, system no.

1 and system no. 2 are simulated using each one of the two ROADM models (simple and dispersive),

that consider two different wavelength selective switches (WSS) models (defined in sub-sections 3.3.2

and 3.3.3). The difference between the simple ROADMs and dispersive ROADMs is that the last (as the

name suggests) distorts the optical signal due to GVD. Each dispersive ROADM introduces 20 ps/nm

of dispersion. This would be equivalent to introduce 1.25 km of fibre per each ROADM (fibre disper-

sion parameter is 16 ps/nm/km). In this work, the longest ROADM chain until the designed maximum

reach is achieved has 23 ROADMs, what is equivalent, from GVD point of view, to 28.8 km of fibre.

These 28.8 km of fibre represent a very short distance when compared to the designed maximum reach

(1850 km). Therefore, it is expected a minimal impact on the system performance. The results are

presented in figures 4.2 and 4.3.

38

Figure 4.2.: Performance comparison of system no. 1 with and without ROADMs (simple and dispersive).

Figure 4.3.: Performance comparison of system no. 2 with and without ROADMs (simple and dispersive).

Both figures (4.2 and 4.3) show that no visible performance difference exists, when simple ROADMs or

dispersive ROADMs are used. This confirms that the dispersion introduced by the ROADMs is too little

to cause any visible impact on the performance. Figure 4.2 shows that the ROADM chain degrades the

performance of system no. 1, while figure 4.3 shows no performance degradation in system no. 2 when

ROADMs are used. The cause for the performance degradation is the filtering of the ROADM chain

(since the dispersion of the ROADMs has no impact), which in system no. 1 (using 32 GHz) causes more

impact than on system no. 2 (using 16 GHz).

The only impact of the ROADMs in system no. 2 is an improvement of the performance for distances

beyond the designed maximum reach when compared to the reference BER curve (without ROADMs).

This improvement is artificial and can be explained. As shown, the impact of the dispersion added by

the ROADMs is neglectful. That leaves the filtering as only cause for this difference. This filtering

only affects the OFDM signal, since in this system implementation the noise is added to the signal

39

at the receivers input by the noise loader. The filtering applied by the chain of ROADMs attenuates

more severely the high frequency components of the signal, such as the aliasing products (as shown

in appendix A) of the CO-OFDM signal, leaving the spectrum within the OFDM channel practically

unchanged. These aliasing products however, contribute to the power of the optical signal launched into

the fibre. When the chain of ROADMs attenuates these products, it consequently reduces the power of

the optical signal. As a result, the noise loader generates noise with a lower power (which is added to a

signal that maintained its original power within the OFDM band). Thus, the power difference between

the OFDM signal and the noise at the input of the receiver is higher. This could explain the performance

difference observed in system no. 2. A way to confirm this would be to place an optical filter at the output

of the coherent optical transmitter, that suppressed the aliasing products power. However, due to lack of

time, it was not possible to confirm this.

4.2. System performance in a real optical link

The real optical link consists of series of optical amplified fibre spans. Each fibre span starts with one

fibre length (which is 80 km long), followed by one erbium doped fibre amplifier (EDFA) and, at the

end, a ROADM is connected.

In this section, the two system variants (no. 1 and no. 2) are simulated considering the same optical

link and their performance is compared. However, given the method to evaluate the performance, which

relies on direct error counting (DEC), the BER values may not be lower than 1 ⋅ 10−4, otherwise the

required simulation time exceeds the dead-line of this work. This has a direct impact on the choice of

the parameters used for the optical link, since they influence directly the OSNR at the receiver and as a

consequence the (BER).

The parameters that directly influence the OSNR are the noise figure of the EDFAs and the optical signal

launched power (the power of the optical signal at the input of the optical fibre of the first span). The

noise figure of an EDFA can be as low as 3.2 dB (for low noise EDFAs) [Agr3], but typically it is

around 5 dB [Jan08-Jan]. The launched power on typical optical systems is above 0 dBm. However,

in [Jan08-Jan] (a CO-OFDM experiment with similar characteristics to the transmission systems of this

work: transmission over SSMF, with fibre spans 82 km long) is mentioned that signals with launched

powers above -5 dBm have a reduced performance due to the influence of fibre nonlinearities after 680 km

of fibre. Since one of the assumptions of this work is that the effects of fibre nonlinearities can be

neglected, the launched power used in this work must not exceed this value. The OSNR along the line is

obtained for both systems, using EDFAs with a noise figure of 5 dB and a launched power of -5 dBm, is

shown in figure 4.4.

40

Figure 4.4.: Evolution of the OSNR per OFDM stream, along the optical link for system no. 1 and no. 2.with and without ROADMs.

Figure 4.4 shows, that the decay of the OSNR is inversely proportional to the number of spans. This

makes sense since the noise power increase gets smaller from one span to the next one (relatively to the

noise power at the previous span): the noise added at each span has the same power, meaning that on the

second span the noise power increases to the double, but on the third span the noise only increases by

one third and on the fourth span by one fourth and so on.

Figure 4.4 also shows, that when no ROADMs are used system no. 1 reaches the threshold OSNR of

19.5 dB (BER ≈ 1.1 ⋅10−4) after the eighth fibre span (at a distance of around 640 km) and that system

no. 2 reaches the threshold OSNR of 19.6 dB (BER ≈ 1.1 ⋅ 10−4) after the fourteenth fibre span (at

a distance of around 1120 km). Inserting the ROADMs in the optical link reduces the OSNR values

by approximately 4.4 dB on both systems. However, the number of spans necessary to obtain a given

difference on the OSNR is proportional to the number of spans considered. In other words: a 3 dB

difference in the OSNR is obtained at the second span, by increasing the number of spans to three, while

to obtain the same 3 dB difference in the OSNR at the tenth span, it is necessary to increase the number

of spans to 22 (see figure 4.4). Since the OSNR threshold is crossed in system no. 1 after 8 spans and in

system no. 2 after 14 spans, the impact of a 4.4 dB on the OSNR is not the same on both systems. The

insertion of the ROADMs reduces the reach in system no. 1 to 3 spans (5 spans reduction) and in system

no. 2 to 5 spans (9 spans reduction).

Figure 4.4 also confirms what was expected in subsection D.2.1: for the same optical link, the OSNR in

system no. 1 is 3 dB lower than in system no. 2. For this motive a better performance is expected for

system no. 2.

Using this optical link, both system no. 1 and system no. 2 are simulated and the BER as a function of the

length of the optical link is obtained. This simulation was ran with and without ROADMs. The results

are shown in figure 4.5.

The first comment to the results shown in figure 4.5 is that the transmission reach of both system no. 1

41

Figure 4.5.: Performance comparison of system no. 1 versus system no. 2.

and no. 2 on a real optical link is much lower than the designed 1840 km.

Figure 4.5 shows that system no. 2 as expected, performs better than system no. 1 but does not reach

further than 1200 km with a BER below 2 ⋅10−4. The longer transmission reaches reported in the liter-

ature [Jan08-Jan, Jan09] did not transmit optical signals with such an wide band. Narrower bandwidths

improve the noise resilience of the system (see section D.2.1 in appendix D), thus reaching the same

BER with lower OSNR values and therefore increasing the reach for the same optical link.

Figure 4.5 confirms the result obtained in figure 4.4 that using ROADMs reduces significantly the trans-

mission reach of the two systems. The transmission reaches of the two systems suffer a reduction of

approximately 450 km (system no. 1) and 850 km (system no. 2) at a BER of 4 ⋅ 10−4. The reason for

the different transmission reach reductions is already explained in the comments to the results presented

in figure 4.4.

The high increase on the BER after the maximum transmission reach is not observed in figure 4.5. This

indicates that the GVD is no longer the dominant cause for bit errors, but instead the noise. This means

that in order to improve the transmission reach of both systems (no. 1 and no. 2), some measures are

suggested:

∙ use EDFAs with lower noise figures and reduce the losses in the optical link,

∙ reduce the bandwidth of the OFDM signals,

∙ increase the launched power,

The first suggestion is not reasonable in already existing optical links, since it might require the replace-

ment of the existing equipment. Even for new optical links this suggestion increases the installation

42

costs.

The second suggestion can be achieved by employing several OFDM channels at lower bit rates and

combine these parallel streams in order to implement the original high bit rate. But that goes against the

motivation of this work.

The draw-back of the third suggestion (increasing the launched power) is that it also increases the impact

of the fibre nonlinear effects. Reducing the peak-to-average power ratio (PAPR) of the OFDM signal

might however, enable some increase on the launched power and therefore improve the transmission

reach without increasing the impact of nonlinear effects.

4.3. Conclusions

The two transmission systems have been analysed in this chapter under several conditions and the fol-

lowing is concluded.

The performances of the two systems under the same OSNR are virtually equal and they both achieve

the designed maximum reach with similar BER values as intended.

It is also concluded that the difference between the two ROADM models has little impact on the perfor-

mance, since no visible difference is observed in the BER values when one model or the other is used.

Although the filtering effect of the ROADM chain has a visible effect on the performance of system no. 1,

for distances shorter than the maximum designed reach, the impact is not very significant (0.5 ⋅10−4 er-

ror rate increase on the BER at 1850 km). Due to the narrow bandwidth of signal of system no. 2, the

filtering effect has no visible impact on the BER values of system no. 2.

System no. 2 clearly shows a performance superior to the performance of system no. 1, mostly due to

the higher OSNR in system no. 2 (caused by the use of PDM, see appendix D). The major cause limiting

the transmission reach in the real optical link is ASE noise and not GVD. In addition, the losses of the

ROADM reduce significantly the transmission reach (by 450 km in system no. 1 and 850 km in system

no. 2). The transmission distances achieved in the real optical link are much shorter than the designed

maximum reach. From the solutions proposed to improve the transmission distance, the suggestion of

reducing the PAPR in OFDM signals so that the launched power can be increased stands out.

43

44

5. Conclusions and future work

In this chapter, the final conclusions of this work are presented, as well as suggestions for future work on

the specific subject of this dissertation.

5.1. Final conclusions

In this work, the impact of reconfigurable optical add-drop multiplexers (ROADM) on the 100 Gbps

coherent optical orthogonal frequency division multiplexing (CO-OFDM) system performance has been

evaluated using numerical simulation. Based on the study of core networks performed in chapter 1, CO-

OFDM was chosen as the best type of OFDM signal to be employed in those networks.

In chapter 2, the equations ruling the characteristics of OFDM signals and coherent optical transmission

were deduced. These equations show that a CO-OFDM signal at 100 Gbps requires a complex trans-

mission system (with a high number of sub-carriers) and occupies a wide bandwidth (32 GHz in system

no. 1). For this reason, a competitive alternative solution using polarization division multiplexing (PDM)

is also considered (system no. 2), in which two OFDM streams at half the data rate are transmitted on

different polarization directions.

In chapter 3, the models of the ROADM (simple and dispersive) are developed from experimental

data supplied by Nokia Siemens Networks. Based on these models, two effects of using a chain of

ROADMs are demonstrated: narrower channel bandwidth (reduction from 42.5 GHz to 32.5 GHz after

25 ROADMs) and higher losses (4.3 dB per ROADM).

In chapter 4, the numerical results show that both transmission systems (no. 1 and no. 2) are able to com-

pensate the dispersion introduced by the maximum length of optical fibre for which they were designed.

It is also shown that when ROADMs are employed, system no. 2 is not affected by the ROADMs filtering

(due to its 16 GHz signal bandwidth) while system no. 1 experiences some slight degradation after 15–

20 ROADMs (increase of 0.5 ⋅ 10−4). Such a long chain of ROADMs exceeds comfortably the typical

number of ROADMs (8-10 ROADMs) [Feu08]. It is also shown that the most limiting factor of using

ROADMs are the losses they introduce. The losses of the ROADM are compensated by an increase of

the EDFAs gain, what increases the power of the noise added by each EDFA. Although indirectly, each

45

ROADM increases the total noise power on the system, what ultimately reduces the maximum transmis-

sion distance (by 450 km in system no. 1 and by 850 km in system no. 2).

The transmission distances achieved in the real optical link are much shorter than the designed maximum

reach. From the suggestions proposed to improve the transmission distance, the reduction of the PAPR

in OFDM signals, so that the launched power can be increased stands out.

5.2. Future work

As a result of the work developed in this dissertation, some suggestions for future work are here pre-

sented:

∙ study of the impact of WSS detuning relative to the optical carrier of CO-OFDM signal,

∙ study of the impact of fibre nonlinearities on CO-OFDM systems at 112 Gbps for ULH,

∙ analysis of the effect of the propagation over two polarization directions along the fibre and of the

effects of polarization-mode dispersion (PMD) on the CO-OFDM performance,

∙ study the use of pre-emphasis to combat the filtering resulting from a chain of ROADMs,

∙ study ways of reducing the peak-to-average power ratio of an CO-OFDM signal and its impact on

the system performance.

46

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51

52

A. Details of the OFDM coder and decoder

In this appendix the description, as well as some related theory, of the elements which implement the

OFDM transmitter and receiver in the simulator is presented.

A.1. Constellation mappers and symbol detectors

The constellation mappers task is first for each group of Nb bits to identify the corresponding data symbol

and then to output the in-phase and quadrature components (I and Q, respectively) according to the used

constellation. A scheme of the constellation mapper is presented in figure A.1.

Figure A.1.: Scheme of the implemented constellation mapper (left) and used constellation (right). Forsimplicity it is presented in this figure an example using quadrature phase shift keying (QPSK), butthe concept can be extended to any other modulation.

The symbol detectors task is to do the opposite of the constellation mapper. This means it outputs a

sequence of Nb bits corresponding to the data symbol whose I and Q are closest to the I and Q present

at the input. The distance from the I and Q components pair present at the input to all the I and Q pairs

present in the data symbol list is done by a distance calculator. The data symbol, that returns the smallest

distance by the calculator, is chosen as the estimation for the transmitted data symbol. A scheme of the

symbol detector is presented in figure A.2. The simulator has three different constellations/modulations

implemented and those are: QPSK, 8-QAM (this modulation is used in [Jan09]) and 16-QAM.

53

Figure A.2.: Scheme of the symbol detector implemented (right), used constellation and received datasymbol (left). For simplicity it is presented in this figure an example with QPSK, but the concept canbe extended to any other modulation.

A.2. DAC and ADC

The simulator runs on a computer, which works with discrete samples. This means it would only be

possible to simulate a continuous reality in a computer if an infinite number of samples was used. This

would require a computer with an infinite large memory, what does not exist. The simulator used in this

work emulates part of the continuous reality by using a number of samples sh f times larger than the

number of samples used in the digital domain. If the bandwidth required by the effects studied in this

work is contained in the simulation bandwidth (bandwidth of the part of the continuous reality that the

simulator emulates), then the number of samples used is high enough. It was considered in this work that

using sh f = 3 was sufficient.

A.2.1. Digital to analog conversion fundamentals

The digital to analog conversion (DAC) process consists in generating a continuous signal from discrete

digital samples. This is implemented with a sample and hold (SH) module followed by a low pass filter

(LPF). For each discrete sample at its input, a continuous signal with the corresponding amplitude is

held constant during one sampling interval at the output. The LPF softens the abrupt changes in the

“staircase” signal at the output of the SH. This process is showed in figure A.3.

54

Figure A.3.: Example of the digital to analog conversion implemented in the simulator. First the discretesignal (left) is fed to the SH. The continuous signal returned by the SH (centre) is then filtered by aLPF resulting in the output signal of the DAC (right).

In signal theory, this SH process is equivalent to convolute the discrete digital samples (delta Diracs with

the corresponding amplitudes) with a filter whose impulse response h(t) is a rectangle of amplitude one

and duration of one sampling interval. The Fourier transform (FT) of h(t) is the transfer function H( f )

of the filter. Since h(t) is a rectangular impulse, H( f ) has a sinc shape. In order to demonstrate this sinc-

effect, the following experiment was conducted: additive white Gaussian noise (AWGN) was digitally

generated and then passed through the SH. As AWGN has a flat spectrum, it is ideal to determine the

transfer function of the SH. The spectrum of the resulting signal has the shape of a sinc function and is

presented in figure A.4. This sinc-effect will be important later, while defining the pre-emphasis function

in section A.4. The DAC process causes also another important effect on the output signal and that is

Figure A.4.: Power spectral density (PSD) of the signal at the output of the SH, for an input of AWGN.The blue curve represents the PSD in a linear scale (so that the sinc shape is easier to recognize) andthe red one represents the PSD in a logarithmic scale.

55

aliasing products generation. The presence of these products in the signal fed to the optical modulator is

not desired and as so the aliasing products must be attenuated. This is achieved by the LPF following the

SH. But the filter used is not ideal, meaning that in order the filtering process to be effective the aliasing

products must be far enough in frequency so that the filter frequency response can decay sufficiently.

Otherwise the aliasing products will be attenuated just as much as the highest frequencies of the OFDM

signal, what is not desirable. For this reason, there is a guard band between the OFDM signal band and

the aliasing products. This guard band is generated by oversampling and the oversampling is achieved

by setting some consecutive high frequency sub-carriers of the OFDM signal to zero.

In other words, the number of sub-carriers set to zero is the parameter that controls the width of that

guard-band and is very important parameter in a OFDM system. The presence of the aliasing products,

together with the sinc-effect and the impact of the number of used sub-carriers in the width of the guard-

band can be seen in figure A.5.

Figure A.5.: OFDM signal in frequency, using 60 % of its sub-carriers (left image) and using 90 % ofits sub-carriers (right image). It is observable that the guard band due to oversampling, is larger inthe case in which 60 % of the sub-carriers are used, compared to the case which uses 90 % of thesub-carriers. The same is to say that the guard band grows wider with the decrease of the number ofused sub-carriers.

A.3. SH, LPF and ADC

About the SH there is not much more to say. The SH used in this work holds for each digital sample at

its input, a amplitude-constant analog signal for sh f +1 sampling periods.

The LPF used at the OFDM coder is a Bessel filter of order 6. The function of this filter is to attenuate

the aliasing products. The LPF used at the OFDM decoder is also a Bessel filter of order 6. The function

of this filter is to limit the amount of noise that is present at the input of the decision device with the

minimum signal distortion possible. For this reason, the cut-off frequency of the LPF at the decoder

56

is quite higher than the one used at the transmitter. The gain of a Bessel LPF of order 6 is shown in

figure A.6. The function of the analog to digital converter (ADC) is to sample the continuous signal and

Figure A.6.: Gain of a 6th order Bessel LPF. The frequency axis is normalized to the cut-off frequency ofthe filter.

generate the corresponding discrete one. The implementation of the ADC in the simulator is achieved

by building a time array using the chosen sampling frequency for the ADC and that covers the interval

of reception (time interval in which the receiver is turned on). Then an output signal array is built with

the same length as the time array. Finally, when the sampling instants of the ADC hit the exact time

instant of one sample of the input signal, then that value is copied to the output signal array. When not,

and the sampling instant of the ADC lies between two samples of the input array, then a interpolation

method is used to generate the sampling value. No quantization errors are considered. A scheme of the

implemented ADC method is presented in figure A.7.

Figure A.7.: Scheme of the implemented ADC method. The analog signal (first row) is the input of theADC and the discrete signal (second row) are the output.

57

A.4. Pre-emphasis and equalizer

In order for OFDM systems to function properly, it is necessary to reduce as much as possible the distor-

tion on the data symbols. From equation 2.3, the data symbols at the receiver output, y(k, i), will always

have distortion (excluding the case of an ideal transmission channel, with H(k, i) = 1, that does not in-

sert distortion). This is the justification to use equalization or pre-emphasis techniques, even if they can

only combat effectively linear distortion effects, such as fibre GDV and DAC distortion (sinc-effect, see

section A.3). Though the objective of the equalizer and the pre-emphasis is the same, equalization and

pre-emphasis operate in two opposite ways. The pre-emphasizer distorts the signal prior and inversely to

the distortion introduced by the transmission system (this distortion comes from any element in the path

of the signal, elements such as the optical fibre, equipment filters and amplifiers). The equalizer receives

the already distorted signal from the transmission system and reduces the effects by applying a inverse

transform at the receivers side. A simple scheme of this two techniques is presented in figure A.8.

Figure A.8.: Pre-emphasis (first row) and equalization (second row) techniques.

In real systems, communication is bidirectional and there is a return channel that can be used to give

the pre-emphasizer at the transmitter information about the transmission channel. In this case both

techniques (pre-emphasis and equalization) are equivalent, being sufficient to use one of them alone.

However, in the simulation the communication is unidirectional, there is no return channel. As a result,

only the equalizer at the receiver has information about the transmission channel and only the equalizer

can combat the channel distortion. Apparently the simulator could work with one single equalizer, but

there are advantages in having both techniques working together in the simulator. Those advantages are:

(1) lower compensation load on each of the techniques (2) and a constant signal to noise ratio (SNR) over

the whole signal spectrum (see figure A.9) in noisy transmission systems. The first advantage is justified

by the fact that the pre-emphasizer can compensate constant sources of distortion such as filters or the

distortion effect of the DAC (sinc-effect, see section 2). By doing so, the load on the equalizer is loosen,

leaving the equalizer with more power to compensate the channel effects. The second advantage spe-

58

cially important in OFDM. Since the OFDM sub-carriers are spread over the spectrum, an non-uniform

SNR means an non-uniform error distribution over the sub-carriers what leads to an overall higher bit

error rate (BER).

Figure A.9.: Pre-emphasis (first row) and equalization (second row) techniques where noise is addedtogether with the distortion. As it can be observed, the SNR on the system using the equalizer is notconstant over the signal spectrum.

As referred in section A.2, during the DAC process there is aliasing products generation. Aliasing prod-

ucts degrade the OFDM signal and need to be attenuated. For that reason a LPF is used after the SH.

However, in order to attenuate these products to a reasonable value, the cut-off frequency of the filter has

to be quite low. This results in a deformation of the OFDM signal. The pre-emphasis module is used to

compensate the attenuation of this filter within the band of the OFDM symbol. The result is an undis-

torted OFDM signal with the power difference between the aliasing products and the high frequency

sub-carriers imposed by the LPF. In other words, the use of the pre-emphasis flattens the frequency re-

sponse of the system within the bandwidth of the OFDM signal while the attenuation of the LPF outside

this band is maintained. This effect is shown in figure A.10.

Figure A.10.: OFDM signal generated by a SH, after a LPF using pre-emphasis (bold black line), after aLPF without using pre-emphasis (black thin line) and directly out of the SH (red dashed line).

59

A.4.1. Pre-emphasis

The pre-emphasizing function (by which the OFDM signal is multiplied) is given by the inverse transfer

function of the series of the two LPF (one at the OFDM coder and the other at the decoder) and the

sinc-effect (due to the SH). This inverse transfer function remains constant as long as the LPF and the

sampling frequency are the same. Thus the pre-emphasizing function saved in the memory of the pre-

emphasizer is constant.

A.4.2. Equalizer

The equalization at the decoder has two steps: (1) capture of the equalization function and (2) equal-

ization of the received OFDM data symbols. The equalization of the OFDM symbols is achieved by

multiplying each sub-carrier by the equalization function, HE(k, i), and HE(k, i) is obtained from the

channel frequency response, H(k, i). When a training symbol (TS) is transmitted, H(k, i) is given by

H(k, i) =y(k, i)ct(k)

, (A.1)

where ct(k) is the training sequence (TSQ) saved in the memory of the decoder (for more information

on the TSQ see section A.7). If equation A.1 is inverted, then HE(k, i) is obtained. However, the even

numbered sub-carriers of the training symbol used in the OFDM implementation described in this work

are nulled. This is because the TS used for synchronism is also used for the equalization and the syn-

chronism algorithm demands that the TS has certain characteristics (see section A.7 for more details).

For those nulled sub-carriers, a interpolation method is used. This method is valid as long as H(k, i) is

continuous (in frequency) and Nsc is big enough (so that the frequency resolution is high and, therefore,

the difference between two consecutive points of H(k, i) is small).

The capture of the equalization function is then obtained by

HE(k, i) =

⎧⎨⎩ct(k)

y(k,i) if k is oddHE (k−1,i)−HE (k+1,i)

2 +HE(k+1, i) if k is even(A.2)

A.5. CP and training symbol modules

The cyclic prefix (CP) module in this work, despite its name, inserts a cyclic extension (CE), which

is the same as using both a CP and a cyclic postfix (CPF), in the OFDM symbol signal. It is shown

that under the same conditions, a better performance is obtained by using CE when compared to using

only CP or CPF (see appendix F). Therefore, the CP-module task is to copy the first NCP and the last

60

NCPF samples of the OFDM signal generated by the inverse fast Fourier transform (IFFT) to generate the

samples of the CPF and the CP signals, respectively, where NCP +NCPF = cTs ⋅Nsc (and cTs is the ratio

between OFDM symbol duration and the duration of the guard interval). Afterwards, it builds the com-

plete OFDM symbol signal by placing the CPF samples at the end and the CP samples at the beginning

of the original OFDM symbol signal. The complete OFDM symbol has a length of Nt samples, where

Nt = (1+ cTs) ⋅Nsc. A schematic of the implemented CP-module is shown in figure A.11.

Figure A.11.: Scheme of the implemented CP-module. The output (complete OFDM symbol) is an arrayof complex numbers whose real and imaginary parts are separated into two arrays that are then sent tothe respective DAC.

The TS is always the same. By this reason, the training symbol module is a memory of length Nt , con-

taining the pre-processed training symbol to be transmitted. The control has the task to switch between

the data signal (leaving the CP-module) and the training symbol signal (saved at the training symbol

module) according to whether a data OFDM symbol is to be transmitted or a TS, respectively. For more

information on the TS, consult section A.7.

A.6. IFFT+P/S and S/P+FFT modules

The IFFT and fast Fourier transform (FFT) are responsible, respectively, for the construction of the

OFDM symbols from the sub-carrier data symbols and recovery of the sub-carriers data symbols from the

OFDM symbol received. The IFFT+P/S module is constituted by a IFFT module followed by a parallel-

to-serial converter (P/S). The task of the IFFT+P/S module is to convert the data symbols returned by the

pre-emphasis module, c′(k, i), into the corresponding OFDM symbol. In other words, this module builds

the OFDM symbols. The scheme of the implemented IFFT+P/S module is presented in figure A.12. The

relation between the sub-carrier index k and the corresponding frequency is given by

fk =

⎧⎨⎩ (k−1) ⋅∆ f k ≤ Nsc/2

(k−Nsc−1) ⋅∆ f k > Nsc/2(A.3)

61

Figure A.12.: Scheme of the implemented IFFT+P/S module. The frequency fs is equal to the full OFDMbandwidth (bandwidth of an OFDM system using 100 % of the sub-carriers).

The S/P+FFT module is constituted by a serial-to-parallel converter (S/P) followed by a FFT module.

The task of the S/P+FFT is to convert the received OFDM symbol, into the sub-carrier symbols (y(k, i)).

A scheme of the S/P+FFT module implemented in the simulator is presented in figure A.13.

Figure A.13.: Scheme of the implemented S/P+FFT module.

62

A.7. OFDM symbol synchronisation at the decoder

As mentioned in subsection 2.1.2, each OFDM frame begins with a TS. The symbol synchronisation

works as follows: (1) first a wide range symbol synchroniser (WRSS) detects an interval of samples in

which the TS begins, (2) the borders of the interval are passed to a fine symbol synchroniser (FSS) that

estimates the correct sample where the training symbol begins, the index of this sample will be called

dbg, (3) after that, the beginning of the nth data symbol within that frame is given by Dbg as shown in

expression A.4 below, (4) the whole process is repeated for the next frames.

Dbg(n) = dbg +Nt ⋅n, n ∈ {1, ...Nsp} (A.4)

where Nsp is the number of data symbols contained in one OFDM frame. The WRSS is a TS detector,

whose estimation of the beginning of the TS is very reliable but has a relatively low precision. The

WRSS uses a simplified implementation of the Schmidl and Cox (SC) algorithm [SC97]. This algorithm

requires the reception of two TS, from which it can determine the beginning of the frame and also correct

a frequency offset (between the carrier of the signal and the signal of the local oscillator) that might exist.

The symbol timing recovery ability relies on searching for the first of the two TS mentioned, which is

a symbol with two identical halves in the time domain. This characteristic will remain identical after

passing through the dispersive channel and this is the reason of its robustness. The detection of these

symbols is achieved by detecting the instants in which the timing metric value, M(d), exceeds a certain

threshold. The definition of M(d) is given by [SC97]

M(d) =∣P(d)∣2

R(d)2 , (A.5)

where P(d) and R(d) are defined in [SC97] as follows

P(d) =

Nsc2 −1

∑m=0

r∗[d +m] ⋅ r[d +m+L], (A.6)

R(d) =

Nsc2 −1

∑m=0∣r[d +m+L]∣2, (A.7)

where r is the array of the samples of the received signal and d is the index of the received sample in

r. However, M(d) does not reach its maximum on one precise peak, which would help to determine

the timing offset with more precision, but instead on a wide time interval (see the time-plateau in figure

A.14). The symbol begins somewhere in this time interval and this is the cause for the lack of precision

in the estimation of the symbol begin mentioned [SC97]. The second training symbol is used to measure

63

Figure A.14.: Timing metric obtained for a stream of OFDM frames (left) and one of its peaks is shownwith improved time resolution (right).

the frequency offset. However, in this work we are only interested in using the SC algorithm to recover

the symbol timing and, therefore, the WRSS described in this work uses a simplified version of the SC

algorithm. In this simplified version, only the first TS is necessary. A scheme of the complete symbol

synchroniser (WRSS+FSS) is shown in figure A.15. For the SC algorithm to work, the first TS must

Figure A.15.: Scheme of the symbol synchroniser. With the purpose of easing the understanding of thefunctioning of the symbol synchroniser, the portions of signal presented as example are on purposelonger than what they would be in reality. The discrete sample, at which the TS begins is given by dbg.

be constituted of two identical signals (two identical halves) as shown in figure A.16 . According to

64

Figure A.16.: Special charactheristic of training symbols for the Schmidl and Cox algorithm: the trainingsymbol must have two identical halves.

[SC97] there are two ways to generate such a TS. One is applying an IFFT with half the window size

to the training sequence and then attach the resulting signal to a copy of itself. The second possibility

(and the one implemented in this work) is to apply the regular IFFT to a training sequence in which

every intercalated sub-carrier training symbol is zero (nulled). Once the TS is generated, it still has to be

processed by the pre-emphasis module and the CP-module before being completed. The scheme of the

TS generation is presented in figure A.17.

Figure A.17.: Scheme of TSQ (top) and TS generation. LR and LL are the number of the two last sub-carriers with data before the sub-carriers nulled for oversampling purposes mentioned in section A.2.1.In this example the constellation used is QPSK.

65

66

B. Elements of the coherent optical transmitter

and receiver

In this appendix the description, as well as some related theory, of the elements with which the coherent

optical transmitter and receiver are implemented are presented.

B.1. Optical and electrical components

B.1.1. Directional coupler

A directional coupler consists of two parallel dielectric waveguides, that are in close proximity to each

other [Agr21]. The coupling process results from the exchange of signal between two waveguides due

to their proximity. A scheme of the directional coupler is shown in figure B.1. The input-output fields

Figure B.1.: Scheme of the directional coupler.

relation of a coupler is given by

⎡⎣u1

u2

⎤⎦=

⎡⎣ √ρ j ⋅

√1−ρ

j ⋅√

1−ρ√

ρ

⎤⎦ ⋅⎡⎣e1

e2

⎤⎦ , (B.1)

where ρ is the power coupling ratio. When ρ = 0.5, then the optical signal is split equally between both

output ports. Such couplers are referred to as 3-dB couplers and are the only kind of couplers used in

67

this work. The input-output field relation of a 3-dB coupler is given by

⎡⎣u1

u2

⎤⎦=1√2⋅

⎡⎣1 j

j 1

⎤⎦ ⋅⎡⎣e1

e2

⎤⎦ . (B.2)

B.1.2. Optical modulator

An optical modulator is a device that modulates an optical carrier according to a modulating electrical

signal. The modulators used in this work modulate the amplitude of the optical carrier (optical amplitude

modulators) and are implemented in this work with Mach-Zehnder modulators (MZM). The used MZM

consist of two 3-dB couplers and two electrically controlled phase-shift devices (optical phase modula-

tors). A scheme of the MZM is shown in figure B.2. The optical carrier signal is split by the first 3-dB

Figure B.2.: Scheme of a MZM modulator.

coupler in two optical signals and inserted in the arms of the MZM (one in each arm). The two optical

signals suffer symmetric phase-shifts (ideally symmetric) imposed by the phase-shift devices on each

arm of the MZM. The output of the phase-shift devices is then recombined by the second 3-dB coupler

in order to form the output signal. This results in constructive (and so increasing the amplitude of the

optical field at the output) or destructive (and so reducing the amplitude of the optical field at the output)

interference depending on the phase difference imposed (which depends on the MZM input voltage).

The input-output relation of the electric fields of the MZM is given by [Agr32]

Cmzm(vr f ,vdc) =Eout(t)Ein(t)

= cos(

π

2 ⋅ vπ

⋅ (vdc + vr f )

), (B.3)

where vdc is the bias voltage of the MZM, vr f is the alternating current (AC) coupled electrical modulat-

ing signal and vπ is the voltage that must be present between the electrodes in order to achieve a phase

difference between the two arms of the MZM of π [Agr32]. In coherent optical transmitters, each MZM

must be able to output an optical carrier with an amplitude ranging from Amax down to −Amax, where

Amax is the maximum output value for the amplitude. In order to do this the bias voltage is set to vπ and

68

equation B.3 simplifies into

Cmzm(vr f ) =Eout(t)Ein(t)

= sin(

π

2 ⋅ vπ

⋅ vr f

). (B.4)

The electrodes of the MZM have frequency dependent losses, which are modelled by a low-pass filter

(LPF) [Bar09]. It is considered that this effect is already accounted for in the LPF at the OFDM coder in

section A.3.

B.1.3. Optical source

As considered in section 2.2.4, the optical source is a diode laser that generates a carrier with a single

frequency and constant amplitude.

B.1.4. Optical filter

The transfer function of the optical filter (OF) used at the receiver is obtained from an existing tunable

OF (the bandwidth of the filter as well as the central frequency can be changed), used at the optical

telecommunications laboratory at IT Lisboa. The transfer function of the OF is obtained as follows:

1. additive white Gaussian noise (AWGN) is applied to an optical spectrum analyser (OSA) and its

power spectral density (PSD) is measured,

2. then this AWGN is applied to the input of the OF, while the output of the OF is measured with the

OSA

3. the bandwidth and the central frequency of the OF are set to the desired values,

4. the spectrum obtained at the output of the OF is normalized to the PSD of the AWGN obtained in

the first step and the resulting spectrum equals the squared modulus of the transfer function of the

OF.

The transfer function is obtained from the OF with a bandwidth of 43.5 GHz and is presented in fig-

ure B.3.

69

Figure B.3.: Transfer function obtained experimentally for the OF with a bandwidth of 43.5 GHz and themodel used (using νc = 21.75 GHz, ng = 2.38 and Hg−0 = 1 in equation 3.11 in subsection 3.3.2).

The model used for the OF is the same defined in subsection 3.3.2 for the WSS. Figures B.3 and B.4

shows how well the model fits the experimental data.

Figure B.4.: Transfer function obtained experimentally for the OF with a bandwidth of 30.5 GHz andthe model used (νc = 15.25 GHz, ng = 1.70 and Hg−0 = 1, respectively, in equation 3.11 in subsec-tion 3.3.2).

However, the bandwidths necessary for the OF used in this work are different. Some attempts were made

to set the tunable OF with the desired bandwidths, perform the measurements and model the respective

OF, but this was not possible. The smallest step allowed by the knob regulating the bandwidth of the

OF was too large to set the bandwidth at the desired values. Based on the good fitting of the model

showed in figures B.3 and B.4, the models for the OF used in the work are obtained by setting the desired

bandwidths in equation 3.11.

70

B.1.5. Photodetector

A photodetector is a device that generates an electrical output signal proportional to the optical intensity

that reaches the detector. The photodetectors used in this work are PIN photodiodes and will be further

mentioned simply as PIN. A PIN generates an electrical current called photocurrent, ipin, proportional to

the optical power of the incident optical signal, ppin. ipin is given by

ipin = ppin ⋅Rλ , (B.5)

where Rλ is the responsivity of the PIN [Agr7]. The power of an optical signal, p, is given by

p = ∣ex(t)∣2 + ∣ey(t)∣2, (B.6)

where ex(t) and ey(t) are the electrical field of the optical signal on perpendicular polarization directions

x and y, respectively.

B.2. Transmitted signal equations

Let the source LD1 generate an optical carrier of amplitude Eld1, optical frequency ω1 and phase φ1. Its

electrical field is given by

eLD1(t) = Eld1 ⋅ e j⋅(ω1t+φ1). (B.7)

The signal eLD1(t) is applied to the input port 1 of a 3-dB coupler when input port 2 has no signal applied.

This results in splitting the signal eLD1(t) over the two outputs equally generating the signals eLI(t) and

eLQ(t) as can be seen in 2.6. The equations of the signals eLI(t) and eLQ(t) are given by

eLI(t) = eLD1(t) ⋅1√2=

Eld1√2⋅ e j⋅(ω1t+φ1). (B.8)

eLQ(t) = eLD1(t) ⋅j√2=

Eld1√2⋅ e j⋅(ω1t+φ1) ⋅ e j π

2 . (B.9)

The signals eLI(t) and eLQ(t) are then applied as optical carriers to the input port of the MZM and

modulated by the electrical signals Ich and Qch (see figure 2.6). The modulated optical signals are the

in-phase and in-quadrature components of the optical signal to be transmitted through the fibre. For this

reason, the optical signal at the output of the MZM in the Q arm is 90o shifted backwards (to compensate

the effect of the 3-dB coupler) to become eQ(t) and being then combined with the signal eI(t) at the

second 3-dB coupler (see figure 2.6). The equations of the optical signals eI(t) and eQ(t) at the input of

71

the coupler are given by

eI(t) = eLI(t) ⋅Cmzm(Ich(t)) =Eld1√

2⋅ e j⋅(ω1t+φ1) ⋅Cmzm(Ich(t)), (B.10)

eQ(t) = eLQ(t) ⋅Cmzm(Qch(t)) =Eld1√

2⋅ e j⋅(ω1t+φ1) ⋅Cmzm(Qch(t)) ⋅ e j π

2 . (B.11)

The complete modulated optical signal emos(t), resulting from the combination of eI(t) and eQ(t), using

a 3-dB coupler, is given by

emos(t) = (eI(t)+ j ⋅ eQ(t)) ⋅1√2=

Eld1

2⋅ e j⋅(ω1t+φ1)

(Cmzm(Ich(t))+Cmzm(Qch(t)) ⋅ e j π

2

). (B.12)

B.3. Received signal equations

At the receiver side, let the source LD2 generate an optical carrier, eLD2(t), with an electrical field of

constant amplitude Eld2, optical frequency ω2 and phase φ2. Its electrical field is given by

eLD2(t) = Eld2 ⋅ e j⋅(ω2t+φ2). (B.13)

It is be assumed that the optical signal at the input of the coherent optical receiver, eors, has a carrier with

a electrical field of constant amplitude Eldr, optical frequency ω1 and phase φE (different from φ1 due to

channel propagation), formally identical to emos(t). eors(t) is then given by

eors(t) = Eldr ⋅ e j⋅(ω1t+φE ) ⋅(

Cmzm(Ich(t))+Cmzm(Qch(t)) ⋅ e j π

2

). (B.14)

The signal eors(t) is applied to the OF (in order to suppress the noise outside the pass-band). Assuming

that the spectrum of eors(t) is within the 0.1-dB bandwidth of the OF (and therefore any attenuation

can be neglected), the signal at the output of the OF, e f ors(t), is equal to eors(t). e f ors(t) is splitted by

means of a 3-dB coupler and gives origin to signals er1(t) and er2(t). eLD2(t) is also split by a 3-dB

coupler. Output u2 of this last 3-dB coupler originates eLD(t) and output u1 is shifted by an external 90o

phase-shifter. The signals er1(t), er2(t) and eLD(t) are given by

er1(t) =e f ors√

2=

Eldr√2⋅ e j⋅(ω1t+φE ) ⋅

(Cmzm(Ich(t))+Cmzm(Qch(t)) ⋅ e j π

2

), (B.15)

er2(t) = j ⋅e f ors√

2=

Eldr√2⋅ e j⋅(ω1t+φE ) ⋅

(Cmzm(Ich(t)) ⋅ e j π

2 −Cmzm(Qch(t))), (B.16)

eLD(t) =j√2⋅ eLD2 = Eld2 ⋅ e j⋅(ω2t+φ2) ⋅ e j π

2 . (B.17)

72

By applying the signals er1(t), er2(t), eLDI(t) and eLDQ(t) to two 3-dB couplers as shown in figure 2.7, the

optical input signals of the four PINs are generated, epin1(t), epin2(t), epin3(t) and epin4(t). The equations

of epin1(t), epin2(t), epin3(t) and epin4(t) are given by

epin1(t)=1√2⋅(er1+ j ⋅eLD)=

e j⋅(ω1t+φE )

2⋅(

Eldr ⋅ [Cmzm(Ich(t))+ j ⋅Cmzm(Qch(t))]−Eld2 ⋅ e j⋅((ω1−ω2)⋅t+φ2−φE )),

(B.18)

epin2(t)=1√2⋅( j ⋅er1+eLD)=

e j⋅(ω1t+φE )

2⋅(

Eldr ⋅ [ j ⋅Cmzm(Ich(t))−Cmzm(Qch(t))]+Eld2 ⋅ e j⋅((ω1−ω2)⋅t+φ2−φE+π

2 )),

(B.19)

epin3(t)=1√2⋅(er2+ j ⋅eLD)=

e j⋅(ω1t+φE )

2⋅(

Eldr ⋅ [ j ⋅Cmzm(Ich(t))−Cmzm(Qch(t))]−Eld2 ⋅ e j⋅((ω1−ω2)⋅t+φ2−φE )),

(B.20)

epin4(t)=1√2⋅( j ⋅er2+eLD)=

e j⋅(ω1t+φE )

2⋅(

Eldr ⋅ [−Cmzm(Ich(t))− j ⋅Cmzm(Qch(t))]+Eld2 ⋅ e j⋅((ω1−ω2)⋅t+φ2−φE+π

2 )).

(B.21)

In order to calculate the output current of the PINs it is first necessary to calculate the optical power of

the signals epin1(t), epin2(t), epin3(t) and epin4(t) (which have all signal energy in one single polarization

direction), which are ppin1(t), ppin2(t), ppin3(t) and ppin4(t) respectively, given by

ppin1(t) = ∣epin1∣2

⇔ ppin1(t) = ∣ ej⋅(ω1t+φE )

2 ⋅(Eldr ⋅ [Cmzm(Ich(t))+ j ⋅Cmzm(Qch(t))]−Eld2 ⋅ e j⋅∆φ(t)

)∣2

⇔ ppin1(t) = Eldr⋅Eld22 ⋅ [−Cmzm(Ich(t)) ⋅ cos(∆φ(t))−Cmzm(Qch(t)) ⋅ sin(∆φ(t))]

+E2

ldr4 ⋅(Cmzm(Ich(t))2 +Cmzm(Qch(t))2

)+

E2ld24

, (B.22)



2 ⋅(

Eldr ⋅ [ j ⋅Cmzm(Ich(t))−Cmzm(Qch(t))]+Eld2 ⋅ e j⋅∆φ(t)+ j⋅ π2)∣2

⇔ ppin2(t) = Eldr⋅Eld22 ⋅ [Cmzm(Ich(t)) ⋅ cos(∆φ(t))+Cmzm(Qch(t)) ⋅ sin(∆φ(t))]

+E2


)+

E2ld24

, (B.23)



2 ⋅(Eldr ⋅ [ j ⋅Cmzm(Ich(t))−Cmzm(Qch(t))]−Eld2 ⋅ e j⋅∆φ(t)

)∣2

⇔ ppin3(t) = Eldr⋅Eld22 ⋅ [−Cmzm(Ich(t)) ⋅ sin(∆φ(t))+Cmzm(Qch(t)) ⋅ cos(∆φ(t))]

+E2


)+

E2ld24

, (B.24)



2 ⋅(

Eldr ⋅ [−Cmzm(Ich(t))− j ⋅Cmzm(Qch(t))]+Eld2 ⋅ e j⋅∆φ(t)+ π

2

)∣2

⇔ ppin4(t) = Eldr⋅Eld22 ⋅ [Cmzm(Ich(t)) ⋅ sin(∆φ(t))−Cmzm(Qch(t)) ⋅ cos(∆φ(t))]

+E2


)+

E2ld24

, (B.25)

73

Note that for simplicity (ω1−ω2) ⋅ t +φ2−φE is replaced by ∆φ(t) in the equations above.

The optical power applied to the PINs has a common value ( E2ldr4 ⋅(Cmzm(Ich(t))2 +Cmzm(Qch(t))2

)+

E2ld24 ).

As a result the photocurrent at the output of the PINs has also this constant term multiplied by Rλ . Such

term has to be removed in order to detect the transmitted electrical signals Ich and Qch. This is achieved by

subtracting the current ipin1 from current ipin2 and by subtracting current ipin4 from current ipin3 obtaining

then the currents ipinI and ipinQ respectively, given by

ipinI = ipin2− ipin1 = Rλ ⋅Eld2 ⋅Eldr ⋅ [Cmzm(Ich(t)) ⋅ cos(∆φ(t))+Cmzm(Qch(t)) ⋅ sin(∆φ(t))], (B.26)

ipinQ = ipin3− ipin4 = Rλ ⋅Eld2 ⋅Eldr ⋅ [Cmzm(Qch(t)) ⋅ cos(∆φ(t))+Cmzm(Ich(t)) ⋅ sin(∆φ(t))]. (B.27)

Under the condition of perfect synchronism mentioned in section 2.2.4, the optical source at the receiver

is synchronised in phase with the received signal (φ2 is equal to φE and ω1 = ω2) then ∆φ equals zero

and equations B.26 and B.27 simplify into

ipinI(t) = Rλ ⋅Eld2 ⋅Eldr ⋅Cmzm(Ich(t)), (B.28)

ipinQ(t) = Rλ ⋅Eld2 ⋅Eldr ⋅Cmzm(Qch(t)). (B.29)

The last step to recover Ich and Qch is to set the correct values of the transimpedance gains GI and GQ so

that

Cmzm(Ich(t)) = GI ⋅ ipinI(t), (B.30)

Cmzm(Qch(t)) = GQ ⋅ ipinQ(t). (B.31)

This is done by the signal processor (see figure 2.7) that sets these gains according to the instant power

of the signals at the output of these gain blocks. Assuming that Ich(t),Qch(t) << vπ (what is usually

the case), then the MZMs are operating within their linear region of operation and that means that

Cmzm(Ich(t)) ≈ Ich(t) and Cmzm(Qch(t)) ≈ Qch(t). These are the signals present at the output of the

coherent optical receiver (see figure 2.7).

B.4. Confirmation of analytical results by simulation

In order to confirm the analytical results presented so far, the system is simulated and the results will be

compared. First the coherent optical transmitter and receiver are implemented in the simulator. Second,

by imposing Cmzm(Ich(t)) = 1 and Cmzm(Qch(t)) = 0, the expected output of currents ipinI and ipinQ is

74

simplified into

ipinI = Rλ ⋅Eld2 ⋅Eldr ⋅ cos(∆φ(t)), (B.32)

ipinQ = Rλ ⋅Eld2 ⋅Eldr ⋅ sin(−∆φ(t)). (B.33)

Third, the value of ∆φ is varied over the range [0;2π] (this is achieved by varying the phase φ2 of LD2

over that same range while the received optical signal maintains its phase, frequency and amplitude

constant). If the results of equations B.32 and B.33 are correct, it is expected that current ipinI outputs a

cosine and that current ipinQ outputs a sine. The phase φE is measured at the simulation so that the value

of ∆φ can be calculated and used to generate a comparison line calculated from equations B.32 and B.33.

The results are presented in figure B.5.

Figure B.5.: Confirmation of equations B.32 and B.33 by simulation. The angle φE used in this simulationwas π rad and the simulation was run over 5 ns.

In figure B.5 it can be seen, that the results obtained by the simulator correspond to the results obtained

from equations B.32 and B.33, what confirms that the calculations developed so far are correct.

B.5. Optical synchronisation

Although the optical sources used in this work are ideal (and synchronised in frequency), the phase

of the received signal depends of several factors (such as the original phase at the transmitter and the

propagation time through all the components involved in the optical transmission). It is most likely in

the simulation, that φE ∕= φ2 what leads to ∆φ ∕= 0. If in equations B.26 and B.27 ∆φ ∕= 0, then ipinI starts

75

getting a contribution from Cmzm(Qch(t)) and ipinQ starts getting a contribution from Cmzm(Ich(t)). This

is an undesired effect and the greater ∆φ , the greater these crossed contributions are. This is the reason

why this optical synchronism is so important.

Since the frequencies and phases of the source signals generated by LD1 and LD2 are constant and do

not drift, optical synchronisation only needs to be performed once at system start-up. During this start-up

and before any OFDM transmission takes place, an optical synchronisation signal is transmitted to the

receiver. This signal consists in transmitting Cmzm(Ich(t)) = 1 and Cmzm(Qch(t)) = 0 (just as it was used

in section B.4). At the receiver, the signal processor uses an iterative algorithm that, based on the signals

ipinI and ipinQ, varies the phase of the signal generated by LD2 (φ2). The value of φ2 that leads to ∆φ = 0

(ipinI to a maximum and ipinQ to zero) is the angle of synchronism. This value is saved in the memory

of the receiver and used for the following OFDM transmission. An example showing the algorithm in

action is presented in figure B.6.

Figure B.6.: Determination of the phase of the incoming optical signal by the iterative algorithm used inthe optical synchroniser at the receiver. The stop condition used in this example is an angle differencebetween the consecutive steps (0.5 ns) smaller or equal than 48 µrad.

76

C. Typical OFDM parameters used in CO-OFDM

systems and system design

In order to simulate a realistic CO-OFDM system, the choice of the values of the parameters of the

OFDM transmitter/receiver is of vital importance. The values used by some authors have been gathered

in table C.1. Other references have been consulted, without major differences to the selected references.

Table C.1.: Typical values used in CO-OFDM systems. *Note that the OFDM signal bandwidth is in baseband.

Sub-carrierNo. of sub- No. of used Sub-carrier Data rate/ Symbol CP Bandwidth/ Guard LPF cut-

References modulation carriers sub-carriers usage OFDM stream duration durationOFDM stream band off freq.

Nsc Nu su Db [Gbps] Ts [ns] [ns] Bo f dm [GHz]* [GHz] [GHz]

[Jan08-Jan] QPSK 256 165 0.64 12.9 25.6 2.7 3.2 3.6 3.5

[Jan09] 8-QAM 1024 751 0.73 15.2 102.4 2.2 7.5 1 -

[Shi08-Apr] QPSK 128 87 0.68 10.7 12.2 1.8 3.6 3.4 3.8

The three references in table C.1 represent the typically used values. In table C.1 it can be seen that the

ratio of used sub-carriers is typically between 60% and 70% for most cases. The experiments referred

in table C.1 used standard single mode fibre (SSMF) for transmissions over thousands of kilometres.

The experimented rates range between 10 Gbps and 15 Gbps. In table C.1 it can be seen that the CP

has a duration from 2% up to 14% of the duration of the symbol and ranges between 2 ns to 3 ns. In

the experiments referred in table C.1, the typical modulation used in the sub-carriers is quadrature phase

shift keying (QPSK) (Nb = 2) and the fast Fourier transform FFT window size is always a power of 2.

Training data occupies typically between 2% to 4% of the whole transmission bits [Jan08-Sep].

In addition to these parameters, there are some restrictions that need to be added, namely:

∙ the bandwidth of the optical signal has to fit in a 44 GHz bandwidth channel and preferably to fit

in a 33 GHz channel, because of the 3-dB and 0.1-dB bandwidths of the optical filters used in this

work (where 3 dB is considered sufficient attenuation to cut-off a signal and 0.1 dB is considered

a reduced attenuation that does not cause any distortion to the signal),

∙ the total bit rate of the system is 112 Gbps,

77

∙ the system is to be used in ultra long haul (ULH) and, therefore, needs a transmission reach greater

than 1000 km.

Taking into account these values, the transport systems described in this work have the target parameters

presented in table C.2.

Table C.2.: Target parameters of the two variants of the OFDM transport system analysed in this work.System no. Bit rate Training symbol CP / OFDM symbol Sub-carrier

per OFDM stream, Db spacing, Nsp duration ratio, cTs usage, su

1 112 Gbps 25 data symbols around 10% around 60%

2 56 Gbps 25 data symbols around 10% around 60%

By using the values of table C.2 in equation 2.8 and several different modulations on the sub-carriers the

corresponding bandwidths for the OFDM signal are shown in figure C.1.

Figure C.1.: Bandwidth of OFDM stream signal carrying a bit rate of 112 Gbps (left graphic) and 56 Gbps(right graphic). Graphics obtained with different modulations for the sub-carriers while varying thecTs ratio.

It can be observed in figure C.1 that in order to fulfil the bandwidth limitations of the optical filters

(mentioned before in this section) the modulation format used on the sub-carriers of system no. 1 (at

112 Gbps) can not be QPSK. The simplest modulation that respects the 44 GHz bandwidth and 33 GHz

0.1-dB bandwidth is 16-QAM. For this reason, the chosen modulation for system no. 1 is 16-QAM.

Although for system no. 2 all the modulations tested generate a signal with a band narrower than 44 GHz,

the simplest modulation that respects the 33 GHz 0.1-dB bandwidth (and therefore suffers a minimal

attenuation) recommendation is 16-QAM. For this reason, the modulation chosen for the sub-carriers in

system no. 2 is also 16-QAM.

Once the modulation format of the sub-carriers is chosen, the OFDM symbol duration, Ts, and guard

interval duration, Gi, have to be calculated.

The guard interval duration affects the amount of GVD the system can endure and therefore the maximum

78

transmission length it can reach. A way to estimate the time delay between the highest and lowest

frequency sub-carriers resulting from the GVD of the optical fibre is shown in [Jan09] and given by

Gi = Dλ ⋅Lkm ⋅Bo f dm ⋅sl

ν02 , (C.1)

where Dλ represents the dispersion parameter of the fibre [s/m/km], Lkm is the length of the fibre [km],

Bo f dm is the bandwidth of the OFDM signal [Hz], sl is the speed of light [m/s], ν0 is the optical central

frequency of the OFDM band [Hz] and Bo f dm ⋅ slν02 is the bandwidth of the OFDM signal expressed in

meters.

By using the values of table C.2 in equation 2.7, considering 16-QAM for the sub-carriers, the results

shown in figure C.2 are obtained. The distance lines in figure C.2 are obtained from equation C.1, con-

sidering an optical frequency of 193.41 THz (corresponding to the central channel of the ITU 50 GHz

channel grid [ITUG694]), SSMF with a dispersion parameter of 16 ps/nm/km and from figure C.1 it is

seen that the occupied optical bandwidth is around 32 GHz (depending on the cTs used) for system no. 1

and around 16 GHz for system no. 2.

Figure C.2.: Duration of guard interval for system no. 1 (left graphic) and no. 2 (right graphic). Graphicsobtained for the target parameters mentioned in this section and several FFT window sizes (rangingfrom 128 up to 4096) while varying the cTs ratio.

In figure C.2 it can be seen that system no. 1 can only have transmission reaches beyond 1000 km and

have a cTs ≈ 10% when using an FFT window of size 4096 (higher FFT window sizes are not considered).

Since system no. 1 and no. 2 are intended to have similar transmission reaches (1850 km), then system

no. 2 needs to use an FFT window of size 1024. The final parameters for system 1 and 2 are presented

in the table C.3. The bandwidth of the used low-pass filter (LPF) is chosen according to their function in

the system (see section A.3). The function of the filters are re-mentioned here for convenience.

The function of LPF at the OFDM coder is to attenuate the aliasing products. The attenuation is consid-

ered sufficient if the power of the aliasing products at the output of the filter is 30 dB below the power

of the highest frequency sub-carrier [Jan08-Jan]. It was observed that using a 6th order Bessel LPF with

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Table C.3.: Parameters of both systems 1 and 2. *Note that the OFDM signal bandwidth is in base band.Modulation FFT No. of used Bit rate per OFDM symbol Guard OFDM signalTraining symbol

System no. of window sub-carriersOFDM stream duration interval bandwidth spacing

sub-carriers size, Nsc Nu Db Ts duration, Gi Nsp

1 16-QAM 4096 2459 112 Gbps 76.7 ns 7.7 ns 16 GHz* 25 data symbols

2 16-QAM 1024 615 56 Gbps 38.3 ns 3.8 ns 8 GHz* 25 data symbols

a -3 dB cut-off frequency of half the bandwidth of the OFDM signal (0.5 ⋅∆ f ⋅ Nsc2 ) complied with this

power difference.

The function of LPF at the OFDM decoder is to limit the amount of noise that is present at the input

of the decision device with the minimum signal distortion possible. It was observed that using a 6th

order Bessel LPF with a -3 dB cut-off frequency equal to the bandwidth of the OFDM signal (∆ f ⋅ Nsc2 )

introduced in the worst case (at the high frequency sub-carriers) little more than 1 dB of attenuation to

the OFDM signal. This is still considered acceptable.

The function of the optical filter (OF) is the same as the LFP at the OFDM decoder (limit the amount

of noise power that is present at the input of the decision device with the minimum signal distortion

possible). For this reason, the bandwidth of the OF is chosen so that the spectrum of the used OFDM

signal fits the 0.1-dB bandwidth of the filter.

The bandwidth of the LPF and OF used on both systems are presented in table C.4.

Table C.4.: Bandwidths of the filters used in the system for both variants system no. 1 and no. 2.LPF at LPF at Optical filter at

System no. OFDM coder, OFDM decoder, coherent optical receiver

(3 dB) (3 dB) 3 dB 0.1 dB

1 13.35 GHz 26.70 GHz 35 GHz 26.36 GHz

2 6.68 GHz 13.37 GHz 17.5 GHz 13.18 GHz

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D. Noise, OSNR and BER

In this appendix, the noise generation, the optical signal to noise ratio (OSNR) measurement and OSNR

imposition (using a noise loader), as well as the bit error ratio (BER) measurement are presented and

explained. In section D.1, the method used to generate the noise added to the OFDM signal is presented.

In section D.2, the OSNR is defined and the method used to measure it as well as the method to impose it

are presented in sections D.2.2 and D.2.3 respectively. The method used to measure the BER is presented

in section D.3.

D.1. Noise generation

As explained in section 2.2.4 the only source of noise considered in this work is optical. The only sources

of optical noise in this work are the erbium doped fibre amplifiers (EDFA). Although the power spectral

density (PSD) of the amplified spontaneous emission noise (ASE) has a dependency with the frequency

and varies over the whole C-band (which is 4400 GHz wide) [Bec99], the bandwidth of the signals used

in this work is so small (less than 50 GHz) that it can be considered that the PSD is constant within the

bandwidth of the signal. As a result, the noise used in this work is modeled as additive white Gaussian

noise (AWGN).

The noise is generated on each polarization direction by a pair of random Gaussian sources (both with

the same average and variance) that produce the in-phase and quadrature components of the noise as

shown in figure D.1.

Figure D.1.: Scheme of noise generation, both in quadrature and in-phase with a total power of Pn.

An EDFA generates noise however, in both polarization directions. This means that the noise generation

of an EDFA is modeled for the simulation with two noise generators as the one shown in figure D.1, each

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generating noise in one polarization with an noise power of Pn = Pn−ed f a ⋅ BsimBre f

, where Pn−ed f a is given by

equation 3.9 and Bsim is the simulation bandwidth. The scheme of noise generation on two polarization

directions is shown in figure D.2.

Figure D.2.: Scheme of noise generation, on two polarization directions.

The simulation bandwidth is the bandwidth which the simulator “sees” and over which the total power

of the AWGN is spread.

D.2. OSNR in the simulator

The transmission system can be simulated in two ways: (1) closer to reality by using an optical fibre

with losses and noisy amplifiers (link in a real optical link), or (2) use noiseless and optical transmission

(by either using a lossless fibre or by using noiseless amplifiers) and a noise loader at the end of the

transmission path at the input of the receiver. The first technique enables to test a system where all

the parameters of the in-line components (such as noise factor and bandwidths) can be defined. In this

simulation, the OSNR at the receiver is measured and the performance of the complete system in any

scenario is evaluated. The second technique can only be used if the system is linear (effects such as fibre

nonlinearities can not be present), but enables a certain OSNR to be imposed at the receiver and test the

performance of the receiver under that same OSNR. Summarizing: the first technique requires a method

to measure the OSNR, while the second requires a method to impose an OSNR.

First, OSNR must be defined. OSNR is the ratio between the average signal optical power, Ps, and the

noise optical power in a reference bandwidth, Bre f , (typically 0.1 nm, or 12.5 GHz at 1550 nm), Pn−re f ,

[Win08-Kaminow] as given by

OSNR =Ps

Pn−re f. (D.1)

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D.2.1. OSNR and SNR

The OSNR is measured in the optical domain at the input of the optical filter (OF) of the CO-RX receiver.

The OFDM stream signal is present in one polarization direction and therefore the signal power is all

contained in that single polarization. In system no. 1 at the input of the OF the noise power is spread over

the two polarization directions, however, in system no. 2, due to the polarization demultiplexer (PD), the

noise is present only in the polarization direction of the OFDM signal (see figure 2.8).

For the same signal power and the same optical path (therefore same noise power), the OSNR in system

no. 1 (accounting for both polarization directions and thus twice the noise power) is 3 dB lower than

the OSNR of system no. 2. This situation however, results in the same SNR (measured at the output of

the CO-RX in the electrical domain). To understand how different OSNRs result in the same SNR, lets

consider two uncorrelated noise components (one in each polarization direction) in equation B.14 so that

the received optical signal with noise is given by

eors(t) = Eldr ⋅ e j⋅(ω1t+φE ) ⋅(

so f dm(t) ⋅ e j π

2 +Nx(t)Eldr

)⋅ ex +Ny(t) ⋅ e j⋅(ω1t+φE ) ⋅ ey, (D.2)

where Nx(t) and Ny(t) is electrical field of the ASE noise on polarization directions ex and ey, respectively

and so f dm(t) = Cmzm(Ich(t))+Cmzm(Qch(t)) ⋅ e j π

2 .

For system no. 1 the noise in both polarization directions is considered while in system no. 2, due to the

PD, the ASE noise in direction ey is eliminated and only the noise in direction ex is considered. Following

the mathematical development shown in section B.3, the electrical field of the signals present at the input

of the PINs is given by

epin1(t) =e j⋅(ω1t+φE )

2⋅ [Eldr ⋅

(so f dm(t)+

Nx(t)Eldr

)−Eld2 ⋅ e j⋅∆φ(t)] ⋅ ex +

Ny(t)2⋅ e j⋅(ω1t+φE ) ⋅ ey, (D.3)

epin2(t) =j ⋅ e j⋅(ω1t+φE )

2⋅ [Eldr ⋅

(so f dm(t)+

Nx(t)Eldr

)+Eld2 ⋅e j⋅∆φ(t)] ⋅ ex + j ⋅

Ny(t)2⋅e j⋅(ω1t+φE ) ⋅ ey, (D.4)

epin3(t) =e j⋅(ω1t+φE )

2⋅ [Eldr ⋅ j ⋅

(so f dm(t)+

Nx(t)Eldr

)−Eld2 ⋅e j⋅∆φ(t)] ⋅ ex + j ⋅

Ny(t)2⋅e j⋅(ω1t+φE ) ⋅ ey, (D.5)

epin4(t)=e j⋅(ω1t+φE )

2⋅[Eldr ⋅

(−so f dm(t)−

Nx(t)Eldr

)+Eld2 ⋅e j⋅(∆φ(t)+ π

2 )]⋅ ex−Ny(t)

2⋅e j⋅(ω1t+φE ) ⋅ ey. (D.6)

where for simplicity ∆φ(t) = (ω1−ω2) ⋅t+φ2−φE . The photodetection is done by PINs, which convert

the optical power of the incident signal into electric current. The optical power of signals epin1(t), epin2(t),

83

epin3(t) and epin4(t) is given by

ppin1(t) = ∣epin1 ⋅ ex∣2 + ∣epin1 ⋅ ey∣2


2 ⋅ [Eldr ⋅(

so f dm(t)+Nx(t)Eldr

)−Eld2 ⋅ e j⋅∆φ(t)]∣2 + ∣Ny(t)

2 ⋅ ej⋅(ω1t+φE )∣2

, (D.7)


⇔ ppin2(t) = ∣ j⋅e j⋅(ω1t+φE )

2 ⋅ [Eldr ⋅(


)+Eld2 ⋅ e j⋅∆φ(t)]∣2 + ∣ j ⋅ Ny(t)

2 ⋅ ej⋅(ω1t+φE )∣2

, (D.8)



2 ⋅ [Eldr ⋅ j ⋅(


)−Eld2 ⋅ e j⋅∆φ(t)]∣2 + ∣ j ⋅ Ny(t)

2 ⋅ ej⋅(ω1t+φE )∣2

, (D.9)



2 ⋅ [Eldr ⋅(−so f dm(t)− Nx(t)

Eldr

)+Eld2 ⋅ e j⋅∆φ(t)]∣2 + ∣− Ny(t)

2 ⋅ ej⋅(ω1t+φE )∣2

. (D.10)

The calculations do not need to be further developed to show that the noise present at the polarization

direction ey (atthis point only in system no. 1) is a common term in equations D.7 to D.10, namely:

∣ − Ny(t)2 ⋅ e

j⋅(ω1t+φE )∣ = ∣ j ⋅ Ny(t)2 ⋅ e

j⋅(ω1t+φE )∣ = ∣Ny(t)2 ⋅ e

j⋅(ω1t+φE )∣. This common term is converted by

the PINs into a common term in the photocurrents (ipin1 to ipin4) and when ipinI and ipinQ are obtained

by subtracting ipin1 from ipin2 and ipin4 from ipin3, respectively (see section B.3) this common term is

eliminated. This complete elimination happens as long as the carrier generated by the optical source at

the receiver, on system no. 1 (D.3a), has exactly the same polarization direction as the incoming OFDM

signal.

The result is that both systems reject the noise present at the orthogonal polarization direction, ey. System

no. 1 eliminates the noise from ey at the coherent reception process while system no. 2 eliminates the

noise from ey at the PD before reaching the OF. For the same signal power and same optical path, the

SNR on both systems is equal (see figure D.3).

(a) system no. 1 (b) system no. 2

Figure D.3.: SNR on both systems. As long as the carrier generated by the optical source at the receiver, onsystem no. 1 (D.3a), has the same polarization direction as the incoming OFDM signal (in this exampleex), the noise in polarization direction ey does not contribute to the total noise power converted byphotodetection. This happens also in system no. 2 (D.3b) but the rejection of the noise of orthogonalpolarization directions is achieved by polarization demultiplexer (PD).

84

Tough as referred in the beginning, equal SNRs do not lead to equal performances. System no. 1 uses

twice the bandwidth of system no. 2, what for the same signal power results in a 3 dB reduction in the

PSD of the OFDM signal of system no. 1, Ns−1, when compared with the PSD of the OFDM signal of

system no. 2, Ns−2, (see figureD.4).

Figure D.4.: OFDM stream signal spectrums of system no. 1 (left blue spectrum) and system no. 2 (rightblue spectrum) with the same AWGN power (orange spectrum).

To achieve the same system performance, Ns−1 = Ns−2, what given the bandwidth difference requires

that system no. 1 increases its signal power to the double (3-dB increase). By performing this power

increase, the OSNR in system no. 1 is also increased 3 dB. As a conclusion, equal system performances

are obtained for equal OSNR values.

D.2.2. OSNR measurement

To understand how the OSNR is measured in a simulation, let us, for the sake of an example, assume that

the PSD at the input of the receiver (before the optical filter) in the simulator is what is shown in figure

D.5.

Figure D.5.: Example of PSD of the received signal at the input of the receiver in the simulation.

85

The relation between Pn−re f and Pn is given by

Pn = Pn−re f ⋅Bsim

Bre f. (D.11)

The OSNR is according to the definition, given by the ratio between Ps and Pn−re f . It is then first

necessary to calculate Ps and Pn−re f . For this to work, it is necessary to have the signal with no noise and

the noise signal separated. This is done by using an extra optical link (identical to the first) to propagate

the noise signal independently as shown in figure D.6. At the end of the link, the average power of the

Figure D.6.: Example of measurement of Ps and Pn−re f in the simulator. The noise signal and signal withnoise propagate separately on identical channels, so that at the receiver side the noise signal and thesignal without noise can be extracted and their average powers obtained.

signal, Ps, is calculated. The noise is first passed through am ideal filter with a bandwidth equal to Bre f

and the average power of this signal (at the output of the filter) is calculated resulting in the noise power

in the reference band, Pn−re f . The signal fed to the CO-OFDM receiver, the “real” received signal so to

say, is obtained by simply adding the OFDM signal to the noise.

It is important to refer, that the noise that reaches the receiver was also filtered by the WSS and does

not possess a constant PSD as shown in figure D.6. However, within the band of the WSS, where no

distortion occurs, this constant characteristic of the PSD is maintained. Since the reference filter is

placed at the centre of that same band, the noise power obtained with the method described in this work

is also valid. The representation of the noise floor in figure D.6 does not show this aspect, for matters of

simplicity.

D.2.3. OSNR imposition technique

The noise loader used to impose the OSNR is a noise source that adds the exact amount of noise to the

optical signal, so that the desired OSNR value is obtained. For this technique to work correctly, the

signal that reaches the noise loader must not have any noise. This is the reason why the amplifiers must

be noiseless as shown in figure D.7. The first step of this technique is to measure the power of the signal

86

Figure D.7.: Example of OSNR imposition in the simulator. Noiseless in-line amplifiers are used, so thatthe only noise added to the signal is due to the noise generator at the receiver input.

without noise, Ps. After obtaining the value of Ps, the value of Pn used at the noise generator is returned

by substituting equation D.1 in equation D.11 as shown in

Pn =Ps

OSNR⋅ Bsim

Bre f. (D.12)

Finally, noise with the power Pn is generated and added to the OFDM stream signal.

D.3. BER estimation

The BER in this work is estimated by a direct error counting (DEC) method. This is a method that

generates its estimation of the BER by counting the number of errored bits at the receiver side and then

divides this number by the number of transmitted bits as it is shown in figure D.8.

Figure D.8.: Scheme of the DEC method used in this work to count the number of errored bits and estimatethe BER of one single simulation run.

The number of transmitted bits determines the precision of the BER estimation. In order to obtain a

good estimation, the precision value has to be below the BER value itself. This is why higher BER

87

need a reduced amount of transmitted bits compared to the case of a lower BER (which requires longer

simulations to obtain enough errored bits and achieve the same BER precision). However, the simulator

has a limited memory and can not run a single simulation that is long enough to measure accurately most

of the BER presented in this work. The solution is to split this long simulation in many independent short

simulations. Since the noise is statistically independent and the transmission is linear, the average of the

BER obtained from all the short simulations is equal to the BER of the long simulation. The total BER

is considered accurate, when the number of accumulated errors on the worst sub-carrier reaches 100.

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E. Validation of CO-OFDM signal simulator

In this appendix, the simulator used in this work is validated. The simulator is first assessed in some

simpler configurations, such as back-to-back and lossless standard single mode fibre (SSMF). After that,

the simulator is set under the conditions of experiments described in two papers and the results are

compared. The system used for the first two tests is system no. 2 (see table 2.1).

E.1. Back-to-back configuration

A back-to-back configuration consists in connecting the transmitter directly to the receiver with a very

short optical fibre (short enough so that it does not affect the optical transmission in any significant

way). In a back-to-back configuration, there is no distortion effects and a very high OSNR (practically

infinite since no amplification is used between the transmitter and receiver). As a result, the received

constellation is practically perfect. The constellation obtained for system no. 2 is shown in figure E.1.

Figure E.1.: Received constellation using system no. 2 in a back-to-back configuration.

89

As it can be seen in figure E.1, the symbols in the received constellation are in their correct positions and

no distortion or noise of any kind is visible. This means that, in back-to-back configuration, the simulator

works (perfectly) as expected.

E.2. Fibre chromatic dispersion compensation

In order to evaluate the simulators resilience against group velocity dispersion (GVD), the second test

consists in a lossless and noiseless optical transmission over an optical fibre. The system is tested for

several fibre lengths. It is expected that the transmission system corrects GVD for all fibre lengths up to

1850 km, which is in theory the maximum transmission distance of system no. 2 (maximum transmission

reach, see appendix C). The obtained received constellations are presented in figure E.2.

Figure E.2.: System no. 2 received constellation for several lengths of SSMF.

90

It can be seen in figure E.2 that the degradation of the received constellation grows with the length of the

optical fibre. Despite this degradation, system no. 2 compensates (even if not completely) the GVD up

to its maximum transmission reach (1850 km) what makes this test a success.

E.3. Replication of experiment 1

The goal of the third test is to evaluate how well does the simulator reproduces the results of the exper-

iment described in [Shi07]. The parameters of the OFDM system considered in [Shi07] and the ones

used in the simulator are gathered in table E.1. The bit error ratio (BER) obtained from the simulation

Table E.1.: Parameters gathered from [Shi07] and the parameters used in the simulator. Some of theparameters used in the simulator are not mentioned in [Shi07] and their values had to be estimated.

Sub-carrier FFT No. of used Data rate OFDM CP OSNR Length Training

modulation size sub-carriers per OFDM symbol duration symbol

Nsc Nu stream, Db duration, Ts Gi [dB] [km] spacing, Nsp

[Shi07] QPSK 128 - 8 Gb/s - 4 ns 13.1 1000 -

simulator QPSK 128 75 8 Gb/s 14 ns 4 ns 13.1 1000 25 data symbols

is 1.7 ⋅10−5 and the BER obtained by [Shi07] is around 2 ⋅10−5. There is a 15% difference between the

two results. If it is taken into account that not all system parameters are mentioned in [Shi07], which

values had to be estimated to be used in the simulator, this difference is neglegible. As so, this test is

considered a success.

E.4. Replication of experiment 2

The second experiment is described in [Jan09] and the simulator is set with the parameters shown in table

E.2. The BER obtained from the simulation is 9.1 ⋅10−4 and the BER obtained by [Jan09] is 1 ⋅10−3. The

Table E.2.: Parameters gathered from [Jan09] and the parameters used in the simulator. Some of theparameters used in the simulator are not mentioned in [Jan09] and their values had to be estimated.

Sub-carrier FFT No. of used Data rate OFDM CP OSNR Length Training

modulation size sub-carriers per OFDM symbol duration symbol

Nsc Nu stream, Db duration, Ts Gi [dB] [km] spacing, Nsp

[Jan09] 8-QAM 1024 520 15.2 Gb/s 102.4 ns 2.2 ns 14 1009 -

simulator 8-QAM 1024 530 15.2 Gb/s 102.4 ns 2.2 ns 14 1009 25 data symbols

difference between the two results is 9% . It is also important to consider that the experiment described

in [Jan09] takes into account several other effects such as polarization effects, such as polarization mode

dispersion (PMD) and polarization dependent losses (PDL), which the simulator does not. These effects,

91

which are beyond the scope of this work, can be the cause for the existing difference. Assuming that this

is the case, this test is considered a success.

E.5. Conclusions

The simulator used in this work showed the compensation of the fibre dispersion and the replication of

the results of two experiments with a BER error not exceeding 15 %. This error can be due to effects

not taken into account by the simulator and differences in parameter values that were not defined by the

authors of the experiments and which values had to be estimated to be used in the simulation. The fibre

dispersion resilience of the simulator up to the expected limits and the simulators 15 % BER error are

considered satisfactory results. Therefore, the simulator is considered as validated.

92

F. Cyclic prefix, postfix and their performance

In this appendix, the performance of the OFDM transmission system using only cyclic prefix (CP) and

using both CP and cyclic postfix (CPF) simultaneously is compared.

Before any performance comparison between using CP or using cyclic extension (CE), CP and CPF

simultaneously, it is vital to characterize the transmission channel used in this work, which is optical

fibre. The group velocity dispersion (GVD) of the optical fibre applies dispersion to the signal. In order

to obtain the impulse response of an optical fibre, the fibre is excited by a delta Dirac impulse. The

duration of the impulse at the output of the fibre is given by the introduced delay between the lowest

and highest frequencies of the impulse (due to GVD) and this delay is given by equation C.1. For a

Dirac impulse with 4.68 ps of duration, it is considered that it occupies approximately a bandwidth of1

4.68⋅10−12 = 213.61 GHz. If this impulse is transmitted at λ0 = 1550 nm, over 10 km, 80 km and

200 km of SSMF, equation C.1 returns that such an impulse should reach durations of 0.27 ns, 2.19 ns

and 5.47 ns respectively. The simulation results shown in figure F.1 confirm these calculations and the

pulse broadening effect due to GVD. In figure F.1 it can be seen that the GVD broadens the Dirac impulse

in time. The SSMF is a physical channel and therefore is a causal channel. But if a receiver synchronizes

itself at the time instant in which the dirac-impulse originally takes place, any channel response before

that instant is seen by the receiver as a non-causal behaviour.

This non-causal behavior has consequences when using a system with only CP or with both CP and CPF

simultaneously (CE). An example of this is shown in figure F.2. It is expected that using CE (CPF+CP)

brings an improvement in the system performance when compared to a system that uses only CP. In

oder to test this, two transmission systems, A and B, are tested under the same conditions. System A

is identical to system no. 2 (see section 2.2.5) and system B is identical to system A except that it

uses only a CP instead of the CE. The results are shown in figure F.3, where for comparison purposes,

a third system variant (system C) that uses empty guard intervals is also shown. As expected, within

the 1850 km limit (theoretical maximal transmission reach of system no. 2, see appendix C), system A

outperforms both system B and C. For distances greater than 1850 km, the delay spread of the channel is

longer than the guard interval between OFDM symbols and inter-symbol interference ISI appears, what

leads to higher BER.

93

Figure F.1.: Response of different lengths of SSMF to a Dirac impulse. The propagation time was notconsidered.

The conclusion is that for communication distances within the maximum transmission reach, using CE

results in a better performance than using only CP or empty guard intervals.

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Figure F.2.: Transmission with CP and CPF (left side) and only with CP (right side) over a dispersivechannel. The symbol synchronisation detects the beginning of the OFDM symbols with a delay ofthe same duration of the channel impulse response. However, there is signal before this instant, whatresults in a non-causal behaviour from the perspective of the receiver. The discrete Fourier transform(DFT) of the extracted signal (on the right side using CE), y(k, i), divided by the channel frequencyresponse, H(k, i), results in the transmitted data symbols c(k, i). The extracted signal (on the left sideusing only CP) does not contain the complete OFDM symbol what results in inter-symbol interference(ISI).

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Figure F.3.: Performance comparison between three versions of system no. 2, where one version usesempty/nulled guard intervals (system C), another version uses only CP (system B) and the third versionuses both CP and CPF (system A), versus the SSMF length.

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